#geometry-and-trigonometry | Mathematics | Page 175

upper karma Jun 15, 2018, 1:54 PM

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No mercy ;-;

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ok so

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it is right angle

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altitude AD

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wait, triangle would be 90 45 45

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right?

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Which one

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urs

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Which triangle lol

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abc

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Ya

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k

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Prove it first tho

mossy vine Jun 15, 2018, 1:58 PM

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I don't think yours is true @upper karma

upper karma Jun 15, 2018, 1:58 PM

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if it is a right triangle

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Oh wut

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Maybe I remembered t wrong

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and isosceles

mossy vine Jun 15, 2018, 1:58 PM

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cause I think that holds for any right-angled triangle

upper karma Jun 15, 2018, 1:58 PM

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2 sides and 2 angles would be equal

mossy vine Jun 15, 2018, 1:58 PM

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D is midpoint of BC, right?

upper karma Jun 15, 2018, 1:59 PM

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Yeah

mossy vine Jun 15, 2018, 1:59 PM

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yeah then it's true for any right-angled triangle

upper karma Jun 15, 2018, 1:59 PM

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AD is always congruent to half the hypotenuse?

mossy vine Jun 15, 2018, 1:59 PM

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yeah

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draw the circumcircle

upper karma Jun 15, 2018, 1:59 PM

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and in a isoscecles right triangle a=b and c=a(sqrt1)

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In a 3,4,5 triangle it has length 12/5

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sqrt2*

mossy vine Jun 15, 2018, 2:00 PM

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D is the circumcentre

upper karma Jun 15, 2018, 2:00 PM

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yeah

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yeah ur right wtf

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so its wrong?

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can't be proven?

mossy vine Jun 15, 2018, 2:00 PM

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its wrong

upper karma Jun 15, 2018, 2:00 PM

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ok then xd

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was i on the right track if it was true?

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Oops GWqlabsSweats let me reword it

mossy vine Jun 15, 2018, 2:01 PM

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you might've been thinking of the altitude rather than the median

upper karma Jun 15, 2018, 2:01 PM

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Uh I think so

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And yeah mudkip

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k

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Is was literally going to reword it with the altitude xd

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I*

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should i just take this course

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https://www.khanacademy.org/math/geometry/hs-geo-transformations

Khan Academy

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

mossy vine Jun 15, 2018, 2:02 PM

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the whole geometry course on it might be a better idea

upper karma Jun 15, 2018, 2:02 PM

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alright

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i have a month tho..

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If you want

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what are the bare essentials

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proofs and what else

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Theorems

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Also mudkip I wanted to introduce you to @edgy fog

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that's it?

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he’s really good at maths : ^)

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Yeah

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bro

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that khan academy course on geometry

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i cannot do that in a month

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i am going to start with congruence

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📎 asdfag.PNG

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what

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how are they not congruent

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no side angles given?

mossy vine Jun 15, 2018, 2:14 PM

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they are similar, but they aren't necessarily congruent

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the definition of congruence is that all corresponding sides and angles are equal

upper karma Jun 15, 2018, 2:15 PM

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so it is wrong bc u don't know sides?

real mulch Jun 15, 2018, 2:15 PM

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I think it's C.

upper karma Jun 15, 2018, 2:15 PM

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but if you knew one of the sides, it would be congruent?

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yes it is c @real mulch

fallen ivy Jun 15, 2018, 2:16 PM

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Yes cubing

upper karma Jun 15, 2018, 2:16 PM

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k gotcha

real mulch Jun 15, 2018, 2:16 PM

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If one pair of corresponding sides match in length, then yes.

upper karma Jun 15, 2018, 2:17 PM

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can you use a calculator in high school geo?

real mulch Jun 15, 2018, 2:17 PM

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Ask your teacher?

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How could we know?

upper karma Jun 15, 2018, 2:17 PM

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my case is

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i am going into 8th grade

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and i want to skip geometry

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i would be taking it which is a ninth grade class

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but i want to be 2 years ahead

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so i am studying before i take my placements in a month

real mulch Jun 15, 2018, 2:19 PM

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So you're in 7th grade, but you want to take geometry in 8th grade so that you won't have to learn it in 9th grade?

upper karma Jun 15, 2018, 2:19 PM

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no i am doing it in the summer

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doing geometry in summer so i don't have to do it in school

real mulch Jun 15, 2018, 2:19 PM

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God... american school system is quite "free".

upper karma Jun 15, 2018, 2:19 PM

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yes

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i am already a year ahead in math

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honestly the american curriculum sucks

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especially the science

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in middle school

fallen ivy Jun 15, 2018, 2:22 PM

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Lol it depends @real mulch at what school and stuff whether you can skip

upper karma Jun 15, 2018, 2:22 PM

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true

fallen ivy Jun 15, 2018, 2:23 PM

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If I had been given the option I wouldn't have done any high school maths and would have spent 4 years doing independent study like I get to do this year

upper karma Jun 15, 2018, 2:23 PM

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thats good

fallen ivy Jun 15, 2018, 2:23 PM

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Since I could have skipped algebra and calc and geometry

upper karma Jun 15, 2018, 2:25 PM

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Wtf

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am i making a good choice if i study hard enough

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Why would you want to skip that

fallen ivy Jun 15, 2018, 2:26 PM

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Because it would have been better to be published by now ¯_(ツ)_/¯

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Also plum I should teach you calx

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*calc

upper karma Jun 15, 2018, 2:27 PM

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.....

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yeah that would be nice :3

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also you want to publish in high school???

fallen ivy Jun 15, 2018, 2:28 PM

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Ye

real mulch Jun 15, 2018, 2:28 PM

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wow

fallen ivy Jun 15, 2018, 2:28 PM

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Planning to see if I can get published this year

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Crossing my fingers

upper karma Jun 15, 2018, 2:28 PM

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god damn

fallen ivy Jun 15, 2018, 2:28 PM

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Probably in some theoretical CS Haskell shit

upper karma Jun 15, 2018, 2:28 PM

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wtf

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so ur doing college in a year?

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Ur junior rn?

fallen ivy Jun 15, 2018, 2:28 PM

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Since I can into those papers

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I'm going into senior year

upper karma Jun 15, 2018, 2:28 PM

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my god >.<

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I just finished highschool this year. I was in a program where we wrote a 4000 word essay on a research topic of our choice. That was the closest I got to "publishing" haha

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lol

mossy vine Jun 15, 2018, 2:29 PM

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EPQ?

upper karma Jun 15, 2018, 2:29 PM

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i suck at papers

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Nah, IB

mossy vine Jun 15, 2018, 2:29 PM

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o fair

fallen ivy Jun 15, 2018, 2:29 PM

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Lol

real mulch Jun 15, 2018, 2:29 PM

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(Fun fact: Haskell, well, that guy is a miracle... He had three names and all of them have been used to name programming languages.)

fallen ivy Jun 15, 2018, 2:29 PM

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Yeah it's great

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Makes sense though I mean

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Lambda calc

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Anyway

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Plum you should dm me if you have any free time I can start teaching you calc

upper karma Jun 15, 2018, 2:33 PM

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Oh cool

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I have a lot of time tonight cus my aunt is letting me stay up to 2 am to watch the world cup

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So I’m just going to do math instead : ^)

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oh what’s your time rn btw

fallen ivy Jun 15, 2018, 2:35 PM

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Wdym

upper karma Jun 15, 2018, 2:35 PM

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Like ur time zone

fallen ivy Jun 15, 2018, 2:35 PM

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Oh it's 9:35 here

upper karma Jun 15, 2018, 2:35 PM

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Am?

fallen ivy Jun 15, 2018, 2:41 PM

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Mm

upper karma Jun 15, 2018, 2:42 PM

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wat

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GWfroggyZoomeyes

real mulch Jun 15, 2018, 2:42 PM

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Mm

upper karma Jun 15, 2018, 2:44 PM

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Ikr

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the world will never know

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thonker

white harness Jun 15, 2018, 2:55 PM

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It is probably AM.

fallen ivy Jun 15, 2018, 2:59 PM

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Am

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Mmhmm as in yes

upper karma Jun 15, 2018, 3:01 PM

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Oh I see thonker

fallen ivy Jun 15, 2018, 3:02 PM

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but yeah just message me and I should be available today

upper karma Jun 15, 2018, 3:03 PM

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Okay nice

upper karma Jun 16, 2018, 1:25 PM

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yo

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would someone like to teach me some geometry

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pm if u can give me a few quesitons

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thonker let me see if I can think of any off the top of my head

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k

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ty

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Oh this is a nice one

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In right angled triangle ABC with hypotenuse BC, a point D is chosen on BC such that AD is the altitude to BC. Prove that BD * CD = AD^2

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so it has to be isosceles

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AD is right down the middle of bd and cd

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which means bd=cd

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which means bd=ad and cd=ad

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correct?

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none of the triangles have to be isosceles

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k

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that ruins everything

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._.

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where do i start

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my given is that ad creates 2 right angles

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what

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i have no idea where to start

fallen ivy Jun 16, 2018, 1:39 PM

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have you drawn a diagram?

upper karma Jun 16, 2018, 1:39 PM

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yeah

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@fallen ivy

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yeah i did

fallen ivy Jun 16, 2018, 1:42 PM

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hm, lets take some thing we know

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we know that
AD * (BD + CD) = BA * CA

upper karma Jun 16, 2018, 1:44 PM

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how did you get that

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oh wait i understand

fallen ivy Jun 16, 2018, 1:46 PM

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Now it's just applications of pythagorean theorem I believe

upper karma Jun 16, 2018, 1:46 PM

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so ADBC=BACA

fallen ivy Jun 16, 2018, 1:46 PM

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yes that's true

upper karma Jun 16, 2018, 1:47 PM

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what

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pythagorean

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so AC^2 + BA^2=BC^2

fallen ivy Jun 16, 2018, 1:48 PM

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True, but you're looking for something that will give you AD^2

upper karma Jun 16, 2018, 1:48 PM

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hmmm

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add triangle DCA and triangle BAD together

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that will add up to AD^2

fallen ivy Jun 16, 2018, 1:50 PM

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how?

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that's untrue

upper karma Jun 16, 2018, 1:50 PM

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really?

fallen ivy Jun 16, 2018, 1:50 PM

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yes

upper karma Jun 16, 2018, 1:50 PM

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if the triangle was isosceles

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wouldn't it be true?

fallen ivy Jun 16, 2018, 1:50 PM

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It's not isosceles

upper karma Jun 16, 2018, 1:50 PM

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alright then

fallen ivy Jun 16, 2018, 1:51 PM

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and even then I'm not sure I'd have to check

upper karma Jun 16, 2018, 1:51 PM

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ok

fallen ivy Jun 16, 2018, 1:51 PM

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So write down some more pythagorean identities

upper karma Jun 16, 2018, 1:51 PM

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DC^2 and DA^2 gives AC^2

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DA^2 and DB^2 give BA^2

fallen ivy Jun 16, 2018, 1:51 PM

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mmhmm

upper karma Jun 16, 2018, 1:52 PM

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and thats all of them

fallen ivy Jun 16, 2018, 1:52 PM

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Next step is an argument by similar triangles

upper karma Jun 16, 2018, 1:52 PM

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huh?

fallen ivy Jun 16, 2018, 1:53 PM

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or actually this might be enough

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yeah it is

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Okay write down all your equations for pythagorean

upper karma Jun 16, 2018, 1:53 PM

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they are above

fallen ivy Jun 16, 2018, 1:53 PM

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no like on your paper

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and stare at it

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the answer should pop out

upper karma Jun 16, 2018, 1:54 PM

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k lemme write

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i don't get it

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AD^2 appears twice

fallen ivy Jun 16, 2018, 1:57 PM

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You know you can add equations right?

upper karma Jun 16, 2018, 1:57 PM

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yeah ik

fallen ivy Jun 16, 2018, 1:57 PM

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Add the equations in which AD^2 appears

upper karma Jun 16, 2018, 1:57 PM

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~~the answer should pop out~~

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famous last words

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:/

fallen ivy Jun 16, 2018, 1:57 PM

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have you added those equations?

upper karma Jun 16, 2018, 1:58 PM

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2AD^2+BD^2_CD^2

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oh

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ummm

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I think the similar triangle method is a lot simpler thonker

fallen ivy Jun 16, 2018, 1:58 PM

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and what's that equal to?

upper karma Jun 16, 2018, 1:58 PM

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=BA^2+CA^2

fallen ivy Jun 16, 2018, 1:58 PM

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@upper karma exploiting pythagoras lol

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and what's BA^2 + CA^2 equal to

upper karma Jun 16, 2018, 1:58 PM

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GWchadThink

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BC^2 :3

fallen ivy Jun 16, 2018, 1:59 PM

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not you plummmm

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but yes

upper karma Jun 16, 2018, 1:59 PM

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it does?

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^_^

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i am so confused

fallen ivy Jun 16, 2018, 1:59 PM

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Pythagoras on the big triangle

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BA^2 + CA^2 = BC^2

upper karma Jun 16, 2018, 1:59 PM

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I AM SO DUMB

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NEVERMIND

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BRB KMS

fallen ivy Jun 16, 2018, 2:00 PM

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2AD^2 + BD^2 + CD^2 = BC^2

upper karma Jun 16, 2018, 2:00 PM

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wow

fallen ivy Jun 16, 2018, 2:00 PM

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now what is BC = ?

upper karma Jun 16, 2018, 2:00 PM

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AD?

fallen ivy Jun 16, 2018, 2:00 PM

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lolwot how'd you get that

upper karma Jun 16, 2018, 2:00 PM

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ewrwe rtl sewjws

fallen ivy Jun 16, 2018, 2:01 PM

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don't guess, reason

upper karma Jun 16, 2018, 2:01 PM

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AD^2

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ya don’t guess uwu

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no

fallen ivy Jun 16, 2018, 2:01 PM

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look at BC on the diagram

upper karma Jun 16, 2018, 2:01 PM

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k

fallen ivy Jun 16, 2018, 2:02 PM

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Instead of just giving an answer, give a reason for it

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Forces you to think about what you've said

upper karma Jun 16, 2018, 2:02 PM

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2AD

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because equations gave that

fallen ivy Jun 16, 2018, 2:02 PM

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how is that so?

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which equations

upper karma Jun 16, 2018, 2:02 PM

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ones with 2ad in it

fallen ivy Jun 16, 2018, 2:03 PM

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which ones I'm not listing all the equations you've written lol

upper karma Jun 16, 2018, 2:03 PM

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lol

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BDsquared plus ADsquared equals BAsquared

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and Cdsquared plus ADsqured equals CAsquals

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if you add them

fallen ivy Jun 16, 2018, 2:03 PM

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Nah

upper karma Jun 16, 2018, 2:04 PM

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if you add them all

fallen ivy Jun 16, 2018, 2:04 PM

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Look at what you just did

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2AD^2 + BD^2 + CD^2 = BC^2

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Is what happens when you add them

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you then concluded that 2AD = BC

upper karma Jun 16, 2018, 2:04 PM

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i give up i have no idea

fallen ivy Jun 16, 2018, 2:04 PM

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Look at the diagram, it's astoundingly simple

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The art of mathematics always lies in seeing what's right before your eyes

upper karma Jun 16, 2018, 2:05 PM

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do i just need to memorize properties of triangles

fallen ivy Jun 16, 2018, 2:05 PM

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no

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This is literally a property of line segments lol

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the simplest property

upper karma Jun 16, 2018, 2:06 PM

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BD plus CD

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is that what you wanted?

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or no

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gosh i need so much help

fallen ivy Jun 16, 2018, 2:10 PM

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Yes

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That's exactly what I wanted

upper karma Jun 16, 2018, 2:10 PM

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wow

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i am dumb

fallen ivy Jun 16, 2018, 2:10 PM

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Now substitute in the equation you have with 2AD^2

upper karma Jun 16, 2018, 2:12 PM

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umm

fallen ivy Jun 16, 2018, 2:12 PM

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2AD^2 + BD^2 + CD^2 = BC^2

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BC = BD + CD

upper karma Jun 16, 2018, 2:13 PM

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3BD^2+3CD^2=BC^2

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wait what

fallen ivy Jun 16, 2018, 2:13 PM

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Lolwat

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How did you do that

upper karma Jun 16, 2018, 2:13 PM

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i dont' even know

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how did u get what u got

fallen ivy Jun 16, 2018, 2:13 PM

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2AD^2 + BD^2 + CD^2 = BC^2 = (BD + CD)^2

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Simple substitution

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Don't overthink it

upper karma Jun 16, 2018, 2:14 PM

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what

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ugh

fallen ivy Jun 16, 2018, 2:14 PM

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What's the what there?

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We took a BC we saw

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And we replaced it with (BD + CD)

upper karma Jun 16, 2018, 2:15 PM

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oh i was doing something completely wrong

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sorry

fallen ivy Jun 16, 2018, 2:15 PM

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Since BD + CD = BC

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Now expand (BD + CD)^2

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It's okay

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Just justify the algebra to yourself

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Don't symbol shuffle

upper karma Jun 16, 2018, 2:16 PM

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that equals AD^2

fallen ivy Jun 16, 2018, 2:17 PM

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How?

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For one it's not true

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So why did you say it

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What reason do you have to believe it

upper karma Jun 16, 2018, 2:17 PM

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wait no

fallen ivy Jun 16, 2018, 2:17 PM

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Already went over this, don't give an answer without a reason

upper karma Jun 16, 2018, 2:17 PM

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i thought it made sense but cancelling out gave 0

fallen ivy Jun 16, 2018, 2:18 PM

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So

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What is (BD+CD)^2 mean

upper karma Jun 16, 2018, 2:18 PM

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hypotenuse squared

fallen ivy Jun 16, 2018, 2:18 PM

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What does ^2 tell you to do

upper karma Jun 16, 2018, 2:18 PM

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square

fallen ivy Jun 16, 2018, 2:18 PM

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Well yes but not that

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Here

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What's (a + b)^2

upper karma Jun 16, 2018, 2:19 PM

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ab^2

fallen ivy Jun 16, 2018, 2:19 PM

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Nope

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Not at all

upper karma Jun 16, 2018, 2:19 PM

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a^2 + b^2

wide prism Jun 16, 2018, 2:19 PM

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Is this channel the closest this discord has to graph theory?

fallen ivy Jun 16, 2018, 2:19 PM

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Nope @upper karma

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Justify the answer

upper karma Jun 16, 2018, 2:20 PM

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distribute

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then it gives a^2 + B^2

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brb few mins

fallen ivy Jun 16, 2018, 2:20 PM

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Nope it doesn’t

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You can't distribute a ^2 over a +

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Common algebra mistake

upper karma Jun 16, 2018, 2:25 PM

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oh

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i dont understand at all

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how do you expand that

fallen ivy Jun 16, 2018, 2:27 PM

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Work it out explicitly

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a^2 = a * a right?

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So (a + b)^2 = (a + b) * (a + b)

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Now you can work out the right hand side by applying distributive property twice

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Or FOIL if you know it

upper karma Jun 16, 2018, 2:29 PM

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a^2 +b^2 + 2ab

fallen ivy Jun 16, 2018, 2:29 PM

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correct

upper karma Jun 16, 2018, 2:29 PM

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foil'ing killed me in algebra

fallen ivy Jun 16, 2018, 2:29 PM

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foil'ing is a terrible way to learn it

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it's a geometrical property ffs

upper karma Jun 16, 2018, 2:29 PM

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rip my math teacher

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.......

fallen ivy Jun 16, 2018, 2:30 PM

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(BD+CD)^2 = ?

upper karma Jun 16, 2018, 2:30 PM

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the correct way to learn it is to do extremely long expansions for fun : ^)

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😄

fallen ivy Jun 16, 2018, 2:30 PM

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...no

upper karma Jun 16, 2018, 2:30 PM

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yaaa

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BD^2 + CD^2 + 2BDCD

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= BC^2

fallen ivy Jun 16, 2018, 2:31 PM

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correct

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now plug into your earlier equation

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2AD^2 + BD^2 + CD^2 = BC^2

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Correct way to learn FOIL BTW

📎 image.jpg

upper karma Jun 16, 2018, 2:32 PM

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so 2AD^2+BC^2=BC^2

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what

fallen ivy Jun 16, 2018, 2:32 PM

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lol well that works

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wait no

upper karma Jun 16, 2018, 2:32 PM

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so 2AD^2=0...........

fallen ivy Jun 16, 2018, 2:33 PM

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BD^2 + CD^2 + 2BDCD = BC^2

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You just claimed BC^2 = BD^2 + CD^2

upper karma Jun 16, 2018, 2:33 PM

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which is wrong.....

fallen ivy Jun 16, 2018, 2:33 PM

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2AD^2 + BD^2 + CD^2 = BC^2
You can't replace BD^2 + CD^2 with BC^2

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so replace BC^2 with what it's equal to

upper karma Jun 16, 2018, 2:33 PM

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ok

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2AD^2 + BD^2 + CD^2 = BD^2 + CD^2 + 2BDCD = BC^2

fallen ivy Jun 16, 2018, 2:34 PM

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yes

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now cancel from both sides

upper karma Jun 16, 2018, 2:34 PM

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How to expand (a+b)^n geometrically GWfroggyZoomeyes

fallen ivy Jun 16, 2018, 2:35 PM

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same method just in n-dimensional space

upper karma Jun 16, 2018, 2:35 PM

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how do i cancel that...

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thonker

fallen ivy Jun 16, 2018, 2:37 PM

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2AD^2 + BD^2 + CD^2 = BD^2 + CD^2 + 2BDCD

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What do you see added on both sides

upper karma Jun 16, 2018, 2:37 PM

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oh

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so 2AD^2=2BDCD

fallen ivy Jun 16, 2018, 2:37 PM

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yep

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and now

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cancel the 2

upper karma Jun 16, 2018, 2:38 PM

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oh ok

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AD^2=BCDC

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that only took an hour

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wow i am so dumb, i need to study a lot

fallen ivy Jun 16, 2018, 2:39 PM

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It was mainly the algebra

upper karma Jun 16, 2018, 2:40 PM

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yeah i forgot everything in 2 weeks

fallen ivy Jun 16, 2018, 2:40 PM

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which tbh indicates to me you don't have the algebra knowledge to go on to geometry

upper karma Jun 16, 2018, 2:40 PM

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i took algebra in 7th grade

fallen ivy Jun 16, 2018, 2:40 PM

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Well yeah but your teacher was shit

upper karma Jun 16, 2018, 2:40 PM

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lol

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regardless i am doing geometry next year

fallen ivy Jun 16, 2018, 2:41 PM

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I would go back and do algebra again if I were you

upper karma Jun 16, 2018, 2:41 PM

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i just wasn't thinking hard enough

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everything was right infront of me

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hm

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but i still couldn't see it

fallen ivy Jun 16, 2018, 2:41 PM

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Most of the mistakes I see from everyone in high school maths is algebra mistakes, no one teaches algebra right

upper karma Jun 16, 2018, 2:41 PM

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rip

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I had a pretty godly algebra teacher thonker

fallen ivy Jun 16, 2018, 2:42 PM

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When people can't understand in Calculus BC that partial fraction decomposition is just solving linear equations 😩

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eh plum, our excursion into proving the FOTC where you could substitute G(a) = 0 into F(a) = G(a) + C

upper karma Jun 16, 2018, 2:42 PM

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can i have another problem

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@fallen ivy what do you think about my algebra/geometry/etc

fallen ivy Jun 16, 2018, 2:42 PM

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does not give me hope

alpine latch Jun 16, 2018, 2:42 PM

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well it’s got a bit more magic to it @fallen ivy

upper karma Jun 16, 2018, 2:42 PM

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...........

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well boys

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it’s time to end messlf

fallen ivy Jun 16, 2018, 2:42 PM

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<3 you plum

upper karma Jun 16, 2018, 2:43 PM

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_<

alpine latch Jun 16, 2018, 2:43 PM

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like setting up the equations is some weird recipe

#

if there’s multiple roots

fallen ivy Jun 16, 2018, 2:43 PM

#

It's not a weird recipe it's literally adding fractions

alpine latch Jun 16, 2018, 2:43 PM

#

it’s not exactly intuitive to me

#

like if there’s a root with multiplicities

#

you need to for whatever reason add its powers

fallen ivy Jun 16, 2018, 2:43 PM

#

multiplicities are harder yeah

#

but it all comes down to adding fractions

alpine latch Jun 16, 2018, 2:43 PM

#

like if 1 is a double root then you’d have A/(x-1) + B/(x-1)², right?

fallen ivy Jun 16, 2018, 2:44 PM

#

yes

#

this is because it could come from either

#

which isn't a hard idea

alpine latch Jun 16, 2018, 2:44 PM

#

I’ve solved such problems before but I don’t see the intuition there

fallen ivy Jun 16, 2018, 2:44 PM

#

partial fraction decomp is all algebra though

#

especially when you have no multiplicities

#

and somehow people in Calc BC struggle with that...

#

@upper karma but seriously how could you not substitute 0 into an equation

upper karma Jun 16, 2018, 2:45 PM

#

....

#

what do you guys think of khan academy

#

;w;

fallen ivy Jun 16, 2018, 2:45 PM

#

khan is hot garbage

upper karma Jun 16, 2018, 2:45 PM

#

I'm currently reading a basic algebra book and there's a part on partial fraction decomp

#

ayyyy

fallen ivy Jun 16, 2018, 2:45 PM

#

:D

upper karma Jun 16, 2018, 2:45 PM

#

alright xd

#

wolf every fucking time someone asks me that I say it sucks ass and then they’re always like But wheyyy??

#

and I’m like cus it does you fuming babon

alpine latch Jun 16, 2018, 2:46 PM

#

hey now khan is occasionally useful to get an intuition for things

upper karma Jun 16, 2018, 2:46 PM

#

fukingI

alpine latch Jun 16, 2018, 2:46 PM

#

it’s just like way too non-rigorous

upper karma Jun 16, 2018, 2:46 PM

#

yeah I use it sometimes too I’m just being overdramatic

alpine latch Jun 16, 2018, 2:46 PM

#

but e.g. I found the videos on thermodynamics very helpful

#

(for the level I had to know it)

mossy vine Jun 16, 2018, 2:46 PM

#

the problems are alright

fallen ivy Jun 16, 2018, 2:46 PM

#

khan doesn't give you the tools to go further in mathematics imo

alpine latch Jun 16, 2018, 2:46 PM

#

(which was like… know what entropy is and understand the carnot cycle)

#

that is certainly true

fallen ivy Jun 16, 2018, 2:47 PM

#

it's a supplement

alpine latch Jun 16, 2018, 2:47 PM

#

but as a supplement it’s p useful

mossy vine Jun 16, 2018, 2:47 PM

#

I've never used the videos, just some of the problems on it

alpine latch Jun 16, 2018, 2:47 PM

#

my main gripe with it is that the videos are too slow

upper karma Jun 16, 2018, 2:47 PM

#

is the geometry section on khan good

alpine latch Jun 16, 2018, 2:47 PM

#

I have to watch them at 1.5 speed

#

to find them bearable

upper karma Jun 16, 2018, 2:47 PM

#

if i want to study before i take the calss

#

Khan Academy how to solve IMO problems part 1 xd

mossy vine Jun 16, 2018, 2:47 PM

#

which I would say are alright, but they probably get repetetive pretty soon

fallen ivy Jun 16, 2018, 2:47 PM

#

Then again most teachers don't give you the tools to go further in mathematics

#

soooo

#

¯_(ツ)_/¯

#

Everyone go read Lockhart's Lament

mossy vine Jun 16, 2018, 2:48 PM

#

that's also true

upper karma Jun 16, 2018, 2:48 PM

#

What’s that

#

Oh yeah wolf can you help me with one of the challenge problems

fallen ivy Jun 16, 2018, 2:48 PM

#

God-tier essay on the problems with mathematics education

#

every student and teacher should read it

#

and yes I might be able to

#

remember I'm not good at them usually :p

upper karma Jun 16, 2018, 2:50 PM

#

Ya but there’s one specifically that deals with function properties that I’m really interested in

slate phoenix Jun 16, 2018, 7:16 PM

#

Hey, does someone have a difficult geometry problem for me?

mossy vine Jun 16, 2018, 7:44 PM

#

what sort of level?#

slate phoenix Jun 16, 2018, 7:58 PM

#

This level.

📎 Problem.png

#

Maybe even harder.

fallen ivy Jun 16, 2018, 8:02 PM

#

Find the 4th homotopy group of the real projective plane

slate phoenix Jun 16, 2018, 8:04 PM

#

??

frosty flame Jun 16, 2018, 8:04 PM

#

i think he is talking about euclidean geometry @fallen ivy

fallen ivy Jun 16, 2018, 8:10 PM

#

jokes

upper karma Jun 16, 2018, 8:24 PM

#

dick memes

fallen ivy Jun 16, 2018, 8:31 PM

#

???

white harness Jun 16, 2018, 8:34 PM

#

The 4th honotopy group of $$\mathbb{P}^2(\mathbb{R})$$ is $$\mathbb{Z}/4\mathbb{Z}$$.

charred spearBOT Jun 16, 2018, 8:35 PM

#

📎 latex.png

fallen ivy Jun 16, 2018, 8:40 PM

#

Should be Z/2Z

mossy vine Jun 16, 2018, 9:02 PM

#

@slate phoenix try stuff from https://bmos.ukmt.org.uk/home/bmolot.pdf

#

the geometry ones, and I mean I guess other ones if you want as well :^)

#

some will be a bit easier, some about the same, some harder

upper karma Jun 16, 2018, 11:00 PM

#

could i have a geometry quesiton not related to proofs?

real mulch Jun 16, 2018, 11:02 PM

#

JustAsk @upper karma

upper karma Jun 16, 2018, 11:02 PM

#

i did llol

#

can u give me one?

real mulch Jun 16, 2018, 11:04 PM

#

Ohh sorry.

#

I misunderstood.

remote bluff Jun 17, 2018, 3:54 AM

#

what's 6*7 ?

upper karma Jun 17, 2018, 3:54 AM

#

Define the * operator first then we talk

fallen ivy Jun 17, 2018, 4:00 AM

#

lol

upper karma Jun 17, 2018, 4:01 AM

#

:3

upper karma Jun 17, 2018, 1:29 PM

#

could i have another geometric problem to prove

mossy vine Jun 17, 2018, 1:30 PM

#

have you done circle theorems?

#

@upper karma

#

because if not, I'll give you the proofs of some of them to do

upper karma Jun 17, 2018, 1:42 PM

#

i haven't

mossy vine Jun 17, 2018, 1:42 PM

#

ok

upper karma Jun 17, 2018, 1:42 PM

#

can u pm

mossy vine Jun 17, 2018, 1:42 PM

#

ya sure

real mulch Jun 17, 2018, 4:12 PM

#

@upper karma for instance, see this picture https://commons.m.wikimedia.org/wiki/File:Power_point_simple.svg and prove that (PT)^2 = PN * PM given that P is an outer point, PT is a tangent line and PNM is a secant line.

upper karma Jun 17, 2018, 5:25 PM

#

could i have a triangle related proof?

real mulch Jun 17, 2018, 5:30 PM

#

Prove the law of cosines?

#

Then prove that |a| * |b| * cos(A) = a1 * b1 + a2 * b2 (where a and b are vectors, |v| denotes the length, a1, a2, b1, b2 are the coordinates, and A is the angle between a and b).

#

Or see this picture ( https://commons.wikimedia.org/wiki/File:Teorema.png ) and prove that f^2 = de, a^2 = cd and b^2 = ce.

#

@upper karma

upper karma Jun 17, 2018, 5:49 PM

#

i don't know trig yet

real mulch Jun 17, 2018, 6:00 PM

#

ohh

#

The right triangle thing stil stands.

#

And you could also prove Heron's formula.

#

@upper karma

upper karma Jun 17, 2018, 6:11 PM

#

whats that @real mulch

real mulch Jun 17, 2018, 6:13 PM

#

Or see this picture ( https://commons.wikimedia.org/wiki/File:Teorema.png ) and prove that f^2 = de, a^2 = cd and b^2 = ce.

upper karma Jun 17, 2018, 6:19 PM

#

i need a simpler one :/

real mulch Jun 17, 2018, 6:19 PM

#

Do you know the Pythagorean theorem?

upper karma Jun 17, 2018, 6:20 PM

#

yes

real mulch Jun 17, 2018, 6:20 PM

#

Do you know how to expand (a+b)^2?

upper karma Jun 17, 2018, 6:21 PM

#

A^2 + B^2 +AB

real mulch Jun 17, 2018, 6:21 PM

#

Then you know everything to prove that f^2 = de.

#

The other kinda follows from that.

upper karma Jun 17, 2018, 6:21 PM

#

ok

#

i have it

#

i think

#

F^2+D^2=A^2

#

F^2+E^2=B^2

#

2F^2+D^2+E^2= C^2

#

2F^2+D^2+E^2=D^2+E^2+2ED

#

2F^2=2ED

#

F^2=ED

real mulch Jun 17, 2018, 6:24 PM

#

Well done.

upper karma Jun 17, 2018, 6:24 PM

#

k

#

i am getting the hang of this

#

could i ahve another one?

real mulch Jun 17, 2018, 6:24 PM

#

The other two? a^2 and b^2?

upper karma Jun 17, 2018, 6:25 PM

#

oh ok

#

A^2+B^2=C^2

#

F^2+D^2=A^2

#

2A^2+B^2=C^2+D^2+E^2

#

A^2+C^2=C^2+D^2+E^2

#

ummm

#

would E^2+D^2 be C^2

real mulch Jun 17, 2018, 6:27 PM

#

No.

#

e+d = c

upper karma Jun 17, 2018, 6:28 PM

#

A^2=D^2+E^2

#

did i mess up

real mulch Jun 17, 2018, 6:29 PM

#

Your equation is not correct.

#

a^2 = d^2 + f^2

upper karma Jun 17, 2018, 6:29 PM

#

k

#

i cant subtract C^2

#

?

real mulch Jun 17, 2018, 6:29 PM

#

From what?

upper karma Jun 17, 2018, 6:30 PM

#

nvm

#

i gtg

#

and how was that wrong?

real mulch Jun 17, 2018, 6:32 PM

#

A^2=D^2+E^2 - that is not correct.

upper karma Jun 17, 2018, 6:35 PM

#

i meant f :/

real mulch Jun 17, 2018, 6:35 PM

#

I don't understand you, sorry.

upper karma Jun 17, 2018, 6:37 PM

#

i meant F^2

#

not E^2

real mulch Jun 17, 2018, 6:38 PM

#

Ahh, I see. Well, there's nothing wrong with it.

#

But maybe that's not the shortest path to the solution.

upper karma Jun 17, 2018, 6:44 PM

#

ok

#

then ratios?

real mulch Jun 17, 2018, 6:45 PM

#

Actually, just look at this equation: a^2 = d^2 + f^2.

#

What is f^2 equal to?

upper karma Jun 17, 2018, 6:58 PM

#

a^2-d^2

real mulch Jun 17, 2018, 6:58 PM

#

And what else?

#

You've just proved it.

upper karma Jun 17, 2018, 7:01 PM

#

what

real mulch Jun 17, 2018, 7:02 PM

#

You've just proved what f^2 equals.

upper karma Jun 17, 2018, 7:03 PM

#

de

real mulch Jun 17, 2018, 7:03 PM

#

Other than a^2 - d^2.

#

Yes.

upper karma Jun 17, 2018, 7:03 PM

#

:/

#

thats what i did at first

real mulch Jun 17, 2018, 7:03 PM

#

a^2 = d^2 + f^2 and f^2 = de, so you could substitute de for f^2.

upper karma Jun 17, 2018, 7:04 PM

#

so a^2= d^2 +de

real mulch Jun 17, 2018, 7:04 PM

#

yes

upper karma Jun 17, 2018, 7:05 PM

#

d^2+de= cd

#

a^2= cd

real mulch Jun 17, 2018, 7:05 PM

#

what

#

d^2+de= cd - how did you get this from a^2= d^2 +de?

upper karma Jun 17, 2018, 7:06 PM

#

idk lol

real mulch Jun 17, 2018, 7:07 PM

#

So what can you do with a^2 = d^2 +de?

#

How can you manipulate the right-hand side to get c*e?

upper karma Jun 17, 2018, 7:09 PM

#

d^2 + d is c

#

?

real mulch Jun 17, 2018, 7:09 PM

#

No.

upper karma Jun 17, 2018, 7:10 PM

#

how? idk how

real mulch Jun 17, 2018, 7:10 PM

#

What happens when you factor out d on the right-hand side?

upper karma Jun 17, 2018, 7:10 PM

#

e

#

d+e

real mulch Jun 17, 2018, 7:11 PM

#

And what is that equal to?

upper karma Jun 17, 2018, 7:11 PM

#

uhhhh

real mulch Jun 17, 2018, 7:11 PM

#

Just look at the picture.

upper karma Jun 17, 2018, 7:11 PM

#

oh

#

c

real mulch Jun 17, 2018, 7:12 PM

#

So what do you get?

upper karma Jun 17, 2018, 7:12 PM

#

c=a^2

real mulch Jun 17, 2018, 7:12 PM

#

What?

#

How does the equation look after you factor out d?

upper karma Jun 17, 2018, 7:12 PM

#

nvm

#

d+e= a^2/d

real mulch Jun 17, 2018, 7:13 PM

#

That's division by d, not factoring d out.

upper karma Jun 17, 2018, 7:13 PM

#

not the same thing?

real mulch Jun 17, 2018, 7:13 PM

#

Not quite.

upper karma Jun 17, 2018, 7:14 PM

#

then what would a^2 turn into

real mulch Jun 17, 2018, 7:14 PM

#

For one thing, division assumes that d != 0, factoring does not.

#

a^2 = d^2 + de
a^2 = d(d+e)
a^2 = dc [since d+e = c]

do you see it now?

upper karma Jun 17, 2018, 7:15 PM

#

yeah

#

ok

#

ill do b^2

#

e^2+f^2=b^2

#

a^2+b^2=c=2

#

a^2+2b^2=c^2+e^2+f^2

#

a^2+2b^2=c^2+b^2

#

a^2+b^2=c^2

#

b^2=c^2-a^2

#

correct so far?

real mulch Jun 17, 2018, 7:23 PM

#

Yes.

upper karma Jun 17, 2018, 7:27 PM

#

b^2=b^2

#

wait what

real mulch Jun 17, 2018, 7:28 PM

#

That is correct.

upper karma Jun 17, 2018, 7:28 PM

#

xd

real mulch Jun 17, 2018, 7:28 PM

#

But we still don't have what we want.

upper karma Jun 17, 2018, 7:28 PM

#

b^2=a^2+b^2-a^2

#

thats what happens after expansion

real mulch Jun 17, 2018, 7:30 PM

#

Just like with a^2, let's start with the equation b^2 = e^2 + f^2 and do the same thing (notice f^2 = de).

upper karma Jun 17, 2018, 7:32 PM

#

c^2-a^2=e^2+de

#

yes?

real mulch Jun 17, 2018, 7:34 PM

#

Yes, but substituting c^2 - a^2 for b^2 is unncessary.

#

You want to express b^2. Why would you get rid of it?

upper karma Jun 17, 2018, 7:34 PM

#

b^2=e^2+de

#

e(d+e)=b^2

real mulch Jun 17, 2018, 7:35 PM

#

And d+e is?

upper karma Jun 17, 2018, 7:35 PM

#

c

real mulch Jun 17, 2018, 7:35 PM

#

SO?

upper karma Jun 17, 2018, 7:35 PM

#

ce=b^2

#

wow

#

lol thanks

#

i need more practice like thid

upper karma Jun 19, 2018, 6:11 PM

#

could i have something to proof

#

that is related to quadrilaterals

real mulch Jun 19, 2018, 6:18 PM

#

Prove that in a parallelogram 2(a^2 + b^2) = e^2 + f^2 where a,b are the sides; and e,f are the diagonals. @upper karma

#

(aka parallelogram law)

upper karma Jun 19, 2018, 6:35 PM

#

where do i start?

real mulch Jun 19, 2018, 6:36 PM

#

Draw a parallelogram and name the sides, etc. Then find two right angle triangles and you're almost done.

#

Hint: try to express e^2 + f^2

upper karma Jun 19, 2018, 6:36 PM

#

k

real mulch Jun 19, 2018, 6:37 PM

#

You might want to draw some extra lines to make those triangles visible...

upper karma Jun 19, 2018, 6:48 PM

#

ok i did that

#

the two triangles make up the parrelerogram

real mulch Jun 19, 2018, 6:53 PM

#

Hint: try to express e^2 + f^2

upper karma Jun 19, 2018, 6:53 PM

#

uhhhh

upper karma Jun 19, 2018, 7:14 PM

#

i don't understand

real mulch Jun 19, 2018, 7:15 PM

#

Try to express e^2 and f^2 using the Pythagorean theorem, and then add them.

upper karma Jun 19, 2018, 7:15 PM

#

oh Esquared plus Fsquared is either Asquared or Bsquared

real mulch Jun 19, 2018, 7:16 PM

#

uhm... not quite

upper karma Jun 19, 2018, 7:16 PM

#

really?

real mulch Jun 19, 2018, 7:17 PM

#

e^2 + f^2 is not a^2, neither b^2

upper karma Jun 19, 2018, 7:17 PM

#

mhmmm

#

are you sure?

real mulch Jun 19, 2018, 7:18 PM

#

I am sure, since the law you want to prove is 2(a^2 + b^2) = e^2 + f^2.

upper karma Jun 19, 2018, 7:18 PM

#

...

#

ummm

#

not on my paper

real mulch Jun 19, 2018, 7:19 PM

#

Then something must be wrong on your paper, because 2(a^2 + b^2) = e^2 + f^2 holds true for all parallelograms.

upper karma Jun 19, 2018, 7:19 PM

#

hmmm

#

📎 JPEG_20180619_142002.jpg

real mulch Jun 19, 2018, 7:20 PM

#

Ohh

#

e and f are the diagonals

upper karma Jun 19, 2018, 7:20 PM

#

uhh

real mulch Jun 19, 2018, 7:20 PM

#

a and b are the sides

upper karma Jun 19, 2018, 7:20 PM

#

what are diagonals then xd

#

i don't understand lol

#

can you send a picture

real mulch Jun 19, 2018, 7:21 PM

#

https://commons.wikimedia.org/wiki/File:Display_size_measurements.png

#

📎 unknown.png

upper karma Jun 19, 2018, 7:23 PM

#

oh ok lol

#

how would i express Esquared and Fsquared

real mulch Jun 19, 2018, 7:25 PM

#

Using the Pythagorean theorem.

upper karma Jun 19, 2018, 7:34 PM

#

the only one i found was E^2+B^2=A^2

real mulch Jun 19, 2018, 7:35 PM

#

Are you sure?

#

eab is not a right triangle

upper karma Jun 19, 2018, 7:38 PM

#

ok i will just use your thing lol

#

mine was different

#

Asquared Plus Bsquared=Esquared

real mulch Jun 19, 2018, 7:39 PM

#

wait

#

that's not correct

upper karma Jun 19, 2018, 7:39 PM

#

Asquared+Bsquared=Fsquared

#

what

real mulch Jun 19, 2018, 7:39 PM

#

abe is not a right triangle

upper karma Jun 19, 2018, 7:39 PM

#

what is lol

#

idk what is and isn't anymore

real mulch Jun 19, 2018, 7:40 PM

#

A little help.

#

📎 unknown.png

upper karma Jun 19, 2018, 7:49 PM

#

what

#

how does that help

past mantle Jun 19, 2018, 9:22 PM

#

what are u trying to prove?

upper karma Jun 20, 2018, 1:13 AM

#

@past mantle

#

2(a^2 + b^2) = e^2 + f^2.

past mantle Jun 20, 2018, 1:38 AM

#

And what kind of proof are u looking for?

#

Isn't it true that e and f are congruent?

upper karma Jun 20, 2018, 1:50 AM

#

umm idk

#

yes they are congruent

#

ok that just made me solve it

#

wait, they aren't congruent

#

i don't think

#

otherwise that wouldn't be a law

past mantle Jun 20, 2018, 1:52 AM

#

Here

#

This could help

#

📎 JPEG_20180619_215244.jpg

#

I assumed that e and f were congruent

upper karma Jun 20, 2018, 1:53 AM

#

if they were congruent it would be way to easy

past mantle Jun 20, 2018, 1:54 AM

#

Well, it's basically congruent, u have a rhombas

#

E and f are diagonals

#

Making e and f congruent

upper karma Jun 20, 2018, 1:54 AM

#

really?

past mantle Jun 20, 2018, 1:54 AM

#

Yes

upper karma Jun 20, 2018, 1:54 AM

#

in a square

past mantle Jun 20, 2018, 1:54 AM

#

I took geometry already

upper karma Jun 20, 2018, 1:54 AM

#

oh ok

#

well then it is easy

#

2e^2=2(A^2+b^2)

#

e^2=A^2+b^2

past mantle Jun 20, 2018, 1:56 AM

#

I said i^2+h^2=b^2 twice and f^2 and e^2 = a^2 twice

#

U can also make I and h, e and f

#

It's a easy proof

#

I can make a flowchart for clearer results

#

But I really don't want to xd

upper karma Jun 20, 2018, 1:57 AM

#

lol

#

i am trying to skip geometry

past mantle Jun 20, 2018, 1:57 AM

#

.

#

It's useful

#

When u get to real analysis and higher

#

And when ur dealing with proofs

upper karma Jun 20, 2018, 1:58 AM

#

Our friend is probably not looking to a math bachelors.

past mantle Jun 20, 2018, 1:58 AM

#

Hmm

#

I can see that

random aspen Jun 20, 2018, 1:59 AM

#

@upper karma Are you preparing for a competition for skipping geometry ?

upper karma Jun 20, 2018, 1:59 AM

#

skip

random aspen Jun 20, 2018, 1:59 AM

#

?

upper karma Jun 20, 2018, 2:00 AM

#

i want to skip it

random aspen Jun 20, 2018, 2:00 AM

#

Geometry is very important in mathematical competitions

upper karma Jun 20, 2018, 2:00 AM

#

that is why i am studying in summer

past mantle Jun 20, 2018, 2:01 AM

#

What if u forget it

random aspen Jun 20, 2018, 2:01 AM

#

You can take WOOT

past mantle Jun 20, 2018, 2:01 AM

#

?

#

What's WOOT

upper karma Jun 20, 2018, 2:01 AM

#

i wont forget

#

i am not like that

#

Yeah, you stay good at this stuff by exercising it though.

#

It's not a memory thing.

#

ye

#

Use it or lose it, baby.

#

so what do i need to learn for proofs

#

properties of shapes?

random aspen Jun 20, 2018, 2:02 AM

#

What are you preparing for ?

past mantle Jun 20, 2018, 2:02 AM

#

SSS SAS AAS CPCTC

#

All of the theorems/axiums

#

And identies

upper karma Jun 20, 2018, 2:03 AM

#

postulate no. 5

past mantle Jun 20, 2018, 2:04 AM

#

NVM

upper karma Jun 20, 2018, 2:04 AM

#

thonker

past mantle Jun 20, 2018, 2:04 AM

#

My geometry teacher also taught precalc and stats

#

He kept asking me calc questions

#

I kept getting them right

#

thonker

upper karma Jun 20, 2018, 2:05 AM

#

nice

#

i just want to skip

#

Yh, 2 bad

#

why?

#

america is very loose

real mulch Jun 20, 2018, 12:08 PM

#

e and f are not congruent

past mantle Jun 20, 2018, 12:31 PM

#

Well diagonals of a rhombas are perpendicular

alpine latch Jun 20, 2018, 12:34 PM

#

things I should probably try to remember: the volume of a sphere has the prefactor 4/3, not the surface

#

that one’s just got 4

upper karma Jun 20, 2018, 12:35 PM

#

Now prove why GWfroggyZoomeyes

alpine latch Jun 20, 2018, 12:36 PM

#

I mean I could do the integrals but like eh

#

I just did a whole physics exercise wrong cause I constantly wrote A(r) = 4/3 π r²

#

instead of 4πr²

upper karma Jun 20, 2018, 12:37 PM

#

:-(

real mulch Jun 20, 2018, 12:57 PM

#

@past mantle it is a parallelogram

upper karma Jun 20, 2018, 7:57 PM

#

ok

#

do i have to remember every single theorem and postulate lmao

real mulch Jun 20, 2018, 8:16 PM

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Most (not all) of the postulates in Euclid's Elements, as far as I know, are just "common sense".

past mantle Jun 20, 2018, 8:24 PM

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It's also known as Euclidean geometry

upper karma Jun 20, 2018, 8:42 PM

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lol

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so just theorems?

edgy fog Jun 20, 2018, 9:18 PM

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shit haven't learned topology, um what are good textbooks that yall rec

mint sandal Jun 20, 2018, 9:29 PM

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@edgy fog Munkres topology

red citrus Jun 20, 2018, 9:45 PM

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@alpine latch dont forget its 4/3pi r cubed 👀

alpine latch Jun 20, 2018, 9:45 PM

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well I was going for an area you know

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areas have squares

red citrus Jun 20, 2018, 9:45 PM

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Oh then 4pi r squared rt

alpine latch Jun 20, 2018, 9:45 PM

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yes I was saying that

red citrus Jun 20, 2018, 9:45 PM

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I just did a whole physics exercise wrong cause I constantly wrote A(r) = 4/3 π r²

alpine latch Jun 20, 2018, 9:45 PM

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yea

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instead of 4

red citrus Jun 20, 2018, 9:45 PM

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Ye

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I thought u wrote V

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Mb

azure dawn Jun 21, 2018, 7:51 PM

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Hello

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Anyone here?

mint sandal Jun 21, 2018, 7:53 PM

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no

paper frost Jun 21, 2018, 7:58 PM

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Go to general chats to chat

slate phoenix Jun 22, 2018, 4:58 PM

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I've solved this by messing with arcs, but is there a simple, more elegant way to prove this?

📎 Problem.png

real mulch Jun 22, 2018, 5:01 PM

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DAE is one line? @slate phoenix

slate phoenix Jun 22, 2018, 5:02 PM

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yes.

twin prawn Jun 22, 2018, 5:09 PM

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What’s R

fallow edge Jun 22, 2018, 5:09 PM

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Radius maybe?

twin prawn Jun 22, 2018, 5:10 PM

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Why is the line DE purposely drawn off center

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Assuming O isn’t just some useless point and is the center of the circle

fallow edge Jun 22, 2018, 5:10 PM

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Yeah

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Probably just part of the problem

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🤷

slate phoenix Jun 22, 2018, 5:12 PM

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O is the center, R is the radius.

twin prawn Jun 22, 2018, 5:13 PM

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So basically you want to show that A = O?

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Because if so it would be very easy

real mulch Jun 22, 2018, 5:14 PM

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Not necessarily.

twin prawn Jun 22, 2018, 5:14 PM

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Since E is on the circle

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I need to think about this tho

past mantle Jun 22, 2018, 7:22 PM

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Create a line AE

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It is basically the same length of the sides of the triangle formed

slate phoenix Jun 22, 2018, 7:30 PM

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AE is already drawn.

past mantle Jun 22, 2018, 7:33 PM

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BE

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That is what I meant

slate phoenix Jun 22, 2018, 7:52 PM

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@past mantle you mean BE=AB?

real mulch Jun 22, 2018, 7:55 PM

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That is not true...

fallow edge Jun 22, 2018, 7:55 PM

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Wouldn’t that require A to be the midpoint of DE?

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Even then...

real mulch Jun 22, 2018, 7:56 PM

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I think so, yes.

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By the way, OA bisects CB into two equal parts.

slate phoenix Jun 22, 2018, 7:58 PM

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although AE does come out to be equal to BE, and the arc BE is sixth of the whole circle.

real mulch Jun 22, 2018, 7:59 PM

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Because AE is the radius.

past mantle Jun 22, 2018, 7:59 PM

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It's true that BE=AB

real mulch Jun 22, 2018, 7:59 PM

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It is not.

past mantle Jun 22, 2018, 7:59 PM

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It is

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Look

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DC=AC and AB

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Making BE=AB

real mulch Jun 22, 2018, 8:01 PM

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The two red lines are clearly not equal.

📎 unknown.png

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(the letters are not correct, but I hope you can see it)

past mantle Jun 22, 2018, 8:03 PM

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That's because ur using 3 circlea

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Circles*

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Not 1

real mulch Jun 22, 2018, 8:03 PM

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I used the circles to determine the points.

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They have nothing to do with anything else.

past mantle Jun 22, 2018, 8:04 PM

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Have u heard of assuming?

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That's what I am assuming

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That DA=AE

real mulch Jun 22, 2018, 8:05 PM

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But that is clearly not true.

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Why would you assume that?

past mantle Jun 22, 2018, 8:05 PM

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...

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Look at the given

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It works for both sides...

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Making CD=BE, thus making DA=AE

real mulch Jun 22, 2018, 8:07 PM

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But CD != DE.

past mantle Jun 22, 2018, 8:07 PM

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How?

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That's clearly 1/2

zenith ember Jun 22, 2018, 8:07 PM

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📎 geogebra-export_1.png

real mulch Jun 22, 2018, 8:07 PM

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It would be equal if A=O.

past mantle Jun 22, 2018, 8:08 PM

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That's not how it went

real mulch Jun 22, 2018, 8:08 PM

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Thank you.

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@zenith ember

zenith ember Jun 22, 2018, 8:08 PM

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That figure meets all the criteria given.

past mantle Jun 22, 2018, 8:08 PM

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Look, let me make a proof that satifys

zenith ember Jun 22, 2018, 8:08 PM

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Good luck, because that figure meets all the criteria given.

real mulch Jun 22, 2018, 8:09 PM

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By the way, @zenith ember, what did you use? Geogebra?

zenith ember Jun 22, 2018, 8:09 PM

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Yes

past mantle Jun 22, 2018, 8:16 PM

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Here

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Diagram is messy

📎 JPEG_20180622_161628.jpg

real mulch Jun 22, 2018, 8:17 PM

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But AB != BE.

fallow edge Jun 22, 2018, 8:17 PM

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So if Samantha’s diagram is correct, how can you prove that AE=R?

real mulch Jun 22, 2018, 8:18 PM

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AE is in fact equal to R, but AB is not equal to BE.

past mantle Jun 22, 2018, 8:18 PM

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Did anyone look at the proper diagram

zenith ember Jun 22, 2018, 8:18 PM

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How is my diagram not proper?

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AB = AC = BC = CD

past mantle Jun 22, 2018, 8:18 PM

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https://cdn.discordapp.com/attachments/326138757474680852/459764244519321601/Problem.png

zenith ember Jun 22, 2018, 8:18 PM

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D, C, B, E are all on the circle centered at O

fallow edge Jun 22, 2018, 8:19 PM

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Oh actually nvm my question

past mantle Jun 22, 2018, 8:19 PM

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So see my reasoning?

zenith ember Jun 22, 2018, 8:19 PM

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Not at all.

past mantle Jun 22, 2018, 8:19 PM

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thonker

zenith ember Jun 22, 2018, 8:19 PM

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I think you're assuming something, then using that assumption to prove that the assumption is correct.

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aka Circular logic.

real mulch Jun 22, 2018, 8:21 PM

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Your third step needs some reasoning. Given that AB = CD, why does that imply that BE = AB?

zenith ember Jun 22, 2018, 8:22 PM

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You also seem to be assuming that A is the center of the circle. It is not.

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Well, it is not -necessarily- the center.

upper karma Jun 22, 2018, 9:57 PM

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Given the coordinates of B and C and the radius for a sphere, how might I find A in a programmatic step-by-stem manner? (No angles given)

📎 image.jpg

mossy vine Jun 22, 2018, 10:06 PM

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well the line to A is the perpendicular bisector of BC

upper karma Jun 22, 2018, 10:10 PM

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yes, and that is easy to calculate

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what about the distance between the intersection and the sphere's surface

real mulch Jun 22, 2018, 10:11 PM

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You want the intersection of the bisector and the sphere.

mossy vine Jun 22, 2018, 10:12 PM

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I mean, you can calculate the midpoint quite easily

upper karma Jun 22, 2018, 10:12 PM

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as said

mossy vine Jun 22, 2018, 10:12 PM

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and A is easy to calculate from that

upper karma Jun 22, 2018, 10:12 PM

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for context, I'm subdividing an icosahedron, breaking each triangle into four

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how would you do that, exactly (probably missing something obvious)

mossy vine Jun 22, 2018, 10:13 PM

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wait, are you given the coordinates of the centre of the sphere :^)

upper karma Jun 22, 2018, 10:14 PM

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yea

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0,0,0

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local coords of course

real mulch Jun 22, 2018, 10:14 PM

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If you have the midpoint, you can just scale the vector.

mossy vine Jun 22, 2018, 10:14 PM

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^

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scale the coordinates you have of the midpoint to have magnitude R

upper karma Jun 22, 2018, 10:19 PM

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ok lets see if I got this right

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midpoint = ( 0.5 * (x2 + x1), 0.5 * (y2 + y1), 0.5 * (z2 + z1))

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then distance btwn midpoint coords and center multiplied by what?

real mulch Jun 22, 2018, 10:23 PM

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R / current_length

upper karma Jun 22, 2018, 10:23 PM

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oh duh ok 😉

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thank you !!!

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now lets hope C# can handle it or else it'll be early port to C++

real mulch Jun 22, 2018, 10:26 PM

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Why couldn't it?

upper karma Jun 23, 2018, 1:14 AM

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heh @real mulch I tried the midpoint already and it ended up with several zeros and the mesh was completely messed up

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Here it is with the basic icosahedron

📎 image.jpg

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Gotta reconfigure the code for rendering, been a while

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📎 image.jpg

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Yeah...

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@real mulch C# has its limitations

edgy fog Jun 23, 2018, 2:17 AM

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thanks for the startup logo

slate phoenix Jun 23, 2018, 6:36 AM

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My problem is still relevant..

zenith ember Jun 23, 2018, 6:53 AM

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I don't see a more elegant solution than the one you came up with.

last otter Jun 23, 2018, 2:22 PM

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hi guys, dumb question but Im confused. I have theorem that the set of homotopy classes of maps from I=[0,1] to path connected space Y has one element. why is fundamental group pi_{0}(Y, x0) not trivial then???

twin prawn Jun 23, 2018, 2:23 PM

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Can you show me that theorem in more detail please?

mint sandal Jun 23, 2018, 2:24 PM

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i assume the homotopy can change the endpoints?

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doesn't keep them fixed

last otter Jun 23, 2018, 2:24 PM

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its exercise actually https://i.imgur.com/jkP1wKI.png

Imgur

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yeah apple apple square youre probably right, in fundamental group we need to preserve endpoints

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thankz man

mint sandal Jun 23, 2018, 2:25 PM

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👌

twin prawn Jun 23, 2018, 2:25 PM

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apple apple square

sterile meteor Jun 23, 2018, 3:05 PM

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📎 unknown.png

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I do not understand how to solve this question.

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Help will be appreciated.

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😃

mint sandal Jun 23, 2018, 3:14 PM

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trigonometry

keen aspen Jun 23, 2018, 5:51 PM

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^^ Find the appropriate trig function that deals with a known angle value and the opposite side of it

austere stratus Jun 24, 2018, 6:08 AM

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the right angle is 90 and triangle = 180

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=pup 180-90-27

charred spearBOT Jun 24, 2018, 6:09 AM

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📎 result.png

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Do more with Wolfram|Alpha pro

Query made by

@austere stratus

austere stratus Jun 24, 2018, 6:09 AM

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is your third angle

covert idol Jun 24, 2018, 6:09 AM

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@austere stratus why would they want that angle?

austere stratus Jun 24, 2018, 6:09 AM

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now you have a ASA case

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yea no need third to solve for x

covert idol Jun 24, 2018, 6:11 AM

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🤔

austere stratus Jun 24, 2018, 6:12 AM

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or one of those lmao

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with three angles and 1 side

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This is AAS plug whats known into law of sines and solve

covert idol Jun 24, 2018, 6:16 AM

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I imagine they're far more likely to know/be learning the standard right angle trig functions than the sine rule

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Especially since there's not much point using sine rule on a right angled triangle

austere stratus Jun 24, 2018, 6:16 AM

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right

upper karma Jun 24, 2018, 2:07 PM

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i really need help with proofs

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and indirect proofs

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if somebody would please help me, pm me

upper sedge Jun 24, 2018, 5:33 PM

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@upper karma Were you helped privately?

upper karma Jun 24, 2018, 5:33 PM

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YES

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yse

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sorry caps lol

upper sedge Jun 24, 2018, 5:34 PM

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Excellent.

upper karma Jun 24, 2018, 5:34 PM

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more help would be appreicated though

upper sedge Jun 24, 2018, 5:34 PM

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No worries, I took them as excitement about success in math: the best kind

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With what may I be of assistance?

upper karma Jun 24, 2018, 5:35 PM

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i usually feel like i am not given enough information to prove something

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what could help with that

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i think just practice with proofs

upper sedge Jun 24, 2018, 5:38 PM

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certainly that can help.
General number sense, pattern matching skills, and an intuitive grasp of standard techniques like induction, contradiction, pigeon hole ...etc. also helpful might be a collection of definitions. Always go back to the definition.

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Most of that comes from exposure and practice. The rest is in the definitions. Did I mention definitions, yet?

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How I tend to prove something: Check for common patterns that I've seen a million times (like induction), and then before doing anything else, expand everything out into the definitions to see if more patterns appear. Play with small subsets of the general idea to look for patterns. Apply results of pattern hunting to great success.

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Is this helpful? @upper karma

upper karma Jun 24, 2018, 5:47 PM

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uh

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i think he's talking about geometry proofs, like proving properties of a triangle, not really like full-fledged algebraic proofs

upper sedge Jun 24, 2018, 5:47 PM

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Oh

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That changes things. Still: definitions

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Theorem lists

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More definitions, and patterns

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Where possible, break the problem into smaller problems

upper karma Jun 24, 2018, 5:51 PM

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ok

thin wasp Jun 26, 2018, 6:41 AM

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Prove that the reciprocals of the altitudes of an arbitrary triangle can form a triangle themselves (i.e. 1/h_a < 1/h_b + 1/h_c, where h_k denotes an altitude)

thin wasp Jun 26, 2018, 7:17 AM

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<@&286206848099549185>

twin prawn Jun 26, 2018, 11:51 AM

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Ah, I think I have it