I need Little help

[winged tangle]

Can someone please draw this triangle for me I don’t understand what it means by under their base equal another

[toxic vessel]

1. Do not ping the Moderators, unless someone is breaking the rules.
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3. Do not ping other members randomly for help.
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5. Wait patiently for a helper to come along.
6. If the Helper has answered your question, remember to thank them with the Mathematics Ranks bot and close the thread with:

+close
Feel free to nominate the person for helper of the week in #helper-nominations
If you're happy with the help you got here, and the server overall, you can contribute financially as well:

[ember quest]

Yeah, to be honest, I'm also not sure what the second part is about.

[winged tangle]

I’m so confused

[winged tangle]

She also made this

That is the notes about that proposition

[ember quest]

Well, that's the first part.

[winged tangle]

What it could mean

I mean like the second part

Is it this way?

[ember quest]

Hm...

I'm still having problems about "equal straight lines".

In what way can lines be equal?

I'm not sure I get that.

[winged tangle]

They mean the sides ig

I’m their length probably

[ember quest]

Hm... Probably. Though the sides aren't lines, but rather line segments.

[ember quest]

I mean, this is probably what they meant...

Not sure, though.

[winged tangle]

Because it’s the only way possible

[opaque pagoda]

This is from Euclid's Elements, Book 1, Proposition 5, which states exactly what is written in the original photo.

When they mention the "equal straight lines", they are referring to the pre-existing equal sides of an isosceles triangle. What they are wanting you to illustrate is an extension of those two sides, which you are allowed to do because of Book 1, Postulate 2.

So, yes, your illustration is correct! Luckily, she didn't ask you to prove the entire proposition, but it still is good to know why you are allowed to do every single step you're doing!

[ember quest]

Oh, that's why it's written so weirdly.

[opaque pagoda]

Yes, it should've been more specific!

[sonic swift]

Does any book besides I have any Postulates?

[sonic swift]

I also don't understand why it's presented "without proof" when Euclid did prove it.

[slim wyvern]

Not explicitly, but modern scholars usually include other postulates which euclid implicitly assumes.

[slim wyvern]

They mean a proof isnt necessary to satisfy the question

For the sake of the school assignment

[opaque pagoda]

Answered perfectly!

[ember quest]

Yeah, that is odd. It's a proposition, not a postulate.

[sonic swift]

What is the question, and why don't they prove it anyway? This is printed, it looks like some kind of answer key.

[opaque pagoda]

The question is to draw the proposition.

No need to prove it, unless they want that extra work. Which I do like, but is not necessary!

[sonic swift]

You forgot to mark that the triangle is isosceles.

[slim wyvern]

Demonstrating a triangle has two equal angles is sufficient in euclidian geometry to demonstrate that it is isoceles.

[opaque pagoda]

You are so smart! I applaud you!

[winged tangle]

This is my lecturer lecture she made like the book into small chapters

[sonic swift]

...except that this proposition clearly uses "isosceles" and "has two congruent angles" differently.

[slim wyvern]

The question isnt really about isoceles triangles. Its essentially just asking them to make a diagram.

IE demonstrate visually what the passage is describing

Thats all

[sonic swift]

...make a diagram containing an isosceles triangle.

[sonic swift]

The passage describes an isosceles triangle.

[winged tangle]

It there are two equal sides surely it’s isosceles triangle

[opaque pagoda]

(Just for the sake of being meticulous, I would go ahead and mark that the two sides are equal)

Yes. So you should go ahead and mark it.

[winged tangle]

I will surely do thanks for your note

[opaque pagoda]

You're welcome!

[sonic swift]

You haven't marked the sides as congruent.

[winged tangle]

like equal you mean right?

[sonic swift]

Technically no. "Congruent" means distinct in space but equal in measure. If two lines were "equal", they'd just be... the same line.

[sonic swift]

Yes.

[opaque pagoda]

Woohoo!

[winged tangle]

Can you please explain what distinct in space do u mean by

[sonic swift]

I mean just what it sounds like. They're in different locations.

[winged tangle]

ohhh

[sonic swift]

They don't overlap.

[winged tangle]

like this

Let me draw it

[winged tangle]

like two different triangles

And they are equal

[sonic swift]

No, their measures are equal.

All their side lengths and angles.

[winged tangle]

so everything

[sonic swift]

Yes.

[winged tangle]

Please do you know any books I can find exercises like this

So I can get ready for my geometry finals

It’s this next Wednesday

[sonic swift]

I mean, the classic canonical text on geometry is The Elements, by Euclid, but I don't know if a student of your level can read and digest it all in two days.

[winged tangle]

I’m a last year math student

[winged tangle]

It’s the next week

not this Wednesday the other one

[opaque pagoda]

Truthfully, it's been a while since I've picked up and dusted off a geometry textbook...

Does you class not have a specific textbook that goes along with your assignments? I don't like that!

Then, I would recommend googling problems that are similar to the exercises depicted, and see if you can find any theorems or problems associated.

[sonic swift]

What does "last year" mean? Because if you're literally struggling to draw standard geometric diagrams...

[winged tangle]

She just use the Euclid book I’m in uni that is what my lecturer do she make the books into small chapters

[winged tangle]

I will graduate this year

[sonic swift]

...yes, but from where was my question, which you have already answered.

[winged tangle]

I just can’t draw plus I’m on my phone and that triangle I did it was like an idea I got quickly and sent it here

[sonic swift]

Traditionally we use a compass and straightedge to construct geometric figures.

That's actually what the first three postulates are all about.

[winged tangle]

like I said I was on my phone studying and that was like an idea so it was in rush and not professional

[opaque pagoda]

So then review the topics covered in "Euclid's Elements" ! Also, go to your teacher's office hours, if you are in college! I find that receiving tutoring will benefit you greatly!

[ember quest]

Hm... "Elements" is very interesting, but I don't think it's a good way to learn geometry in our time.

As for office hours, you can just mail your teacher, in which case hours don't usually matter.

[winged tangle]

I will try that thank youuu

[winged tangle]

She is so busy😭

[ember quest]

Well, that's the whole point of e-mail - you can answer when you have time.

[opaque pagoda]

Since the exam covers the postulates and propositions mentioned in the text, I would assume that it would be helpful! Either way, just try to find resources that will correspond with what you are learning!

[ember quest]

Oh, yeah, I forgot about that. Well, in that case, maybe it could be used.

[sonic swift]

I like it for its clear axiomatic approach. Too many students fail to learn axiomatic method because modern teachers don't tend to teach it.

[winged tangle]

yesss

[winged tangle]

the questions she said will be outside the lecture but some questions will be inside the lecture and she said the questions outside the lecture you can proof or solve them by using the proposition postulates we learnt

[winged tangle]

like this 2 questions

[sonic swift]

I mean, yeah. The postulates are the fundamental axioms of Euclidean geometry, that's why it's called Euclidean geometry.

[winged tangle]

And if I’m being honest

[sonic swift]

In fact, non-Euclidean geometries are characterized specifically by their divergence from the postulates.

[winged tangle]

I’m terrified

[sonic swift]

Hyperbolic geometry, for instance, rejects the fifth postulate.

[ember quest]

Yeah, and so does spherical. Easier to grasp how it works.

[sonic swift]

Technically no.

[ember quest]

What do you mean?

[sonic swift]

The classical statement of the fifth postulate still holds in spherical geometry, it's just trivial.

All lines intersect in spherical geometry, therefore in particular lines that satisfy the hypothesis of the fifth postulate do.

[ember quest]

Hm. I was under the impression that the fifth postulate depends on the curvature of space that it describes.
If we have a line and a point on it, then the number of lines passing through it parallel to the first line can be:
0 (spherical geometry)
1 (Euclidean geometry)
∞ (hyperbolic geometry)

[sonic swift]

That's not the fifth postulate.

[ember quest]

Wait, what?

Then what is it?

[sonic swift]

That's the modern parallel postulate.

[ember quest]

I've always heard of it as just that.

[opaque pagoda]

It is Wednesday. Not today. Why are you terrified? Just start studying.

Also, I recognize some of Euclid's postulates being used to prove problem 1 on that paper! I'm sure I could say the same about the other two!

[sonic swift]

The fifth postulate states this; given two lines, construct a third line which crosses both. If the sum of the interior angles the two lines make on the same side of the third is less than two right angles, then the two lines intersect on that side of the third.

[ember quest]

Oh. Well, that's equivalent, isn't it?

[sonic swift]

Do you not see how this statement of the postulate is trivially satisfied by spherical geometry?

[ember quest]

Oh, yeah, that's true...

Well, then that form isn't really useful.

I prefer the form I know.

[winged tangle]

I don’t know I got scare when she said some questions would be like you find the measure of an angle by the propositions we learnt

[sonic swift]

The "form you know" isn't logically equivalent, it's stronger.

[sonic swift]

That sounds like just angle chasing.

[ember quest]

Oh, ok.

[opaque pagoda]

So then find the measure! It will be especially easier if some measures are already given. I suggest studying up on angle relations, then, if you are so uncertain.

[sonic swift]

A logically equivalent axiom would be Playfair's axiom; "In a plane, given a line and a point not on it, at most one line parallel to the given line can be drawn through the point."

[ember quest]

Ohh, I see.

[winged tangle]

I did study alot and I even got 9/10 in my quiz but I’m just nervous

[opaque pagoda]

I don't see why you're afraid, then! The more you are certain about what you are learning, the more confident you will become when it comes test-taking time!

[winged tangle]

May I ask how you are so smart do you do like a lot of exercise

[opaque pagoda]

Okay, you said you were confused on Book 1, Proposition 13, correct? Here is what it states:

"If a straight line stands on a straight line, then it makes either two right angles or angles whose sum equals two right angles."

Does that make sense?

[winged tangle]

actually this one

[opaque pagoda]

You flatter me too much. But that second answer is yes; I find that I have to study twice as hard to achieve the results that someone who might find math to be a breeze would achieve.

[winged tangle]

I personally study alot and I get distracted easily but I love studying it’s not like I hate it

But I have A problem

Which is if I’m studying something and I can’t understand a proposition or a postulate I would pick on my myself a lot

[opaque pagoda]

Aha!!! Your teacher is wrong! That is PROPOSITION 12!

[winged tangle]

ohhh

[opaque pagoda]

Open up your textbook again, and try drawing it out!

[winged tangle]

Okay I will draw it on my phone again don’t judge please😭

[opaque pagoda]

This is not art class; I'm not judging!

[winged tangle]

But I don’t understand what she means by a given point not on it

Like from another point?

[ember quest]

Yeah, just a point that doesn't lie on the line.

[winged tangle]

Then how it will be perpendicular

like to that straight line

[sonic swift]

...why couldn't it be?

[ember quest]

Well, if you have a line and a point not on it, you can pretty obviously draw a line perpencidular to the first one.

(or at any angle, really, if you want)

[winged tangle]

Since it’s not on it it says not a point on it

[sonic swift]

I'm confused about how you're interpreting the statement.

[winged tangle]

to me

[slim wyvern]

Think about a 2d plane

[sonic swift]

Every line which is distinct from some given line passes through points not on the given line.

[winged tangle]

It says like draw a line perpendicular to a given line on a point that is not on that given line

[slim wyvern]

You can draw an infinite line stretching off to infinity anywhere on it

[sonic swift]

That's what makes them distinct.

[sonic swift]

No, through a point that is not on it.

[winged tangle]

like we name the point?

[sonic swift]

Look. Picture a line, and a point not on the line.

[slim wyvern]

You could if you wanted

[winged tangle]

OH WAIT LIKE THIS

[sonic swift]

Now, there are infinitely many lines passing through that point, right?

[ember quest]

Yeah.

[sonic swift]

...not OP.

[opaque pagoda]

Hey, stop!!

[winged tangle]

C was a point not on line AB and we extended AB since it’s infinite FORVER

[opaque pagoda]

STOP! Let her solve it!

[sonic swift]

...n9o.

[sonic swift]

Look.

[winged tangle]

Ohhhhh

[sonic swift]

Picture an infinite line and a point that isn't on that infinite line.

There are infinitely many infinite lines that pass through that point.

[slim wyvern]

^ and importantly infinitely many that pass through that line at a perpendicular angle.

[sonic swift]

...no.

[winged tangle]

Thank you so much for your effort I get it now

I thought about whole different thing

[slim wyvern]

For any given line and point combination you can draw another line that intersects both the point and the first line at a perpendicular angle to the original line

Placed anywhere on an infinite plane

It is always the case you can do this

[sonic swift]

...except the whole point was for you to be able to draw the picture yourself.

[opaque pagoda]

I AGREE! I am not pleased with your method of teaching!

[sonic swift]

So they kind of just solved the problem for you, which is against the rules.

They don't even have a helper role.

[opaque pagoda]

I am not satisfied with how she has learned the problem, because you just gave her the answer! Do not do this again, please.

[winged tangle]

She just tried to help please don’t get mad at her

She probably didn’t know

[opaque pagoda]

I am not angry, I am just dissatisfied, because the whole point is for you to critically-think about this problem yourself.

[sonic swift]

<@&1283689826742440016> We have someone without even a helper role presenting full solutions.

[winged tangle]

she probably didn’t know

[dapper matrix]

who?

[winged tangle]

No please I don’t want her to get muted because of me

[opaque pagoda]

That's okay to make a mistake the first time, but I do not want to see this happening again.

[ember quest]

@slim wyvern , please provide hints to a solution instead of a full solution.

[sonic swift]

Motives: Unknown.

[dapper matrix]

yeah, a verbal warning suffices here

[sonic swift]

And also, they maybe shouldn't be helping without a helper role?

[winged tangle]

Please forgive her this time she probably didn’t know

[sonic swift]

I couldn't even pull him aside in #helper-staff because of it.

[dapper matrix]

i disagree

[ember quest]

And I don't care. Does that role even do anything?

[sonic swift]

Grants access to #helper-staff.

[dapper matrix]

access to #helper-staff and gives helper points

[slim wyvern]

Apologies. I thought it seemed like a communication issue.

[ember quest]

Oh, that's it? Yeah, that doesn't matter then.

[sonic swift]

Except that I wasn't able to address him in #helper-staff in order to address this issue.

[winged tangle]

Can I still have this help open until my exam please?

[opaque pagoda]

Communication issue or not, you don't ever just give them the answer. That defeats the whole purpose of her being prepared to pass the test with her own knowledge.

Nevertheless, I appreciated you input on Euclidean geometry, it is clear that you know your stuff.

[winged tangle]

I want to revise all the notes here

[opaque pagoda]

I am not sure about the rules on that, but if you're allowed to, please do so! I would be happy to help you.

[coral carbon]

@slim wyvern it's fine but don't do it again

If we can agree on that, let's move on

[winged tangle]

Hi rion can I please have this help open until exam

[coral carbon]

Yes, fine by me

[ember quest]

Sure, that's up to you.

[winged tangle]

I would appreciate it a lot thank you so much

[winged tangle]

Thank you so much

thank you guys all I can’t mention you guys because they told me I can’t

[coral carbon]

Well generally it is preferred if you close it

Because you can always access this post even after closing

[winged tangle]

Really?

[coral carbon]

But I figured you might have other inquiries

So it's ok, leave it open until after your exam

[winged tangle]

thank you so muchhhhhh

[coral carbon]

Yes, you can access this post even after closing it, as long as you have the link

https://discord.com/channels/624314920158232616/1333107394053673070

[winged tangle]

It doesn’t open but since you allowed me to let it still open it’s okay again thank you all

[coral carbon]

👍

[winged tangle]

Using axiomatic system is my answer correct for this theorem

[indigo marsh]

natural numbers are actually sequences

[winged tangle]

What that means please can you elaborate

[indigo marsh]

I'm so sorry, when I messaged here discord glitched and I thought I was in #math-discussion , this is not relevant to your question in any way

[winged tangle]

Oh you scared me 😭it’s okay don’t worry

[winged tangle]

Poli can you please help me

[opaque pagoda]

Howdy hey! I’m in class right now; I’ll get back to you shortly!

[opaque pagoda]

Hm. Is this “Theorem 7” mentioned anywhere in “Euclid’s Elements”? Someone feel free to correct me, but this looks like a combination of Young’s Theorem 7 & 9, which states “there are exactly nine points” and “there are exactly twelve lines", respectively.

I find this to be interesting, because you are using the propositions and postulates of Euclid to prove a theorem which I'm pretty sure was stated by John Wesley Young. I don't know if you're allowed to do this, but I will look into this further.

So is Euclid's method the only method that you are learning in class? Or has your instructor mentioned other mathematician's practices of geometry? Because I am certain that you would have to use previously stated axioms and theorems of Young to prove this here theorem (7 & 9).

Also, I am thoroughly confused. Why on earth has your teacher combined these two theorems and labeled it as "theorem 7"? That is just plain wrong!

[winged tangle]

Sorry I just saw your respond

so actually I thinks she did this for more practice

and after this theorem

like in theorem 14 it says that

[opaque pagoda]

Can you show me the entire sheet that has all the theorems for your class? And answer my first inquiry, please. Is “Euclid’s Elements” the only textbook you are utilizing for this course?

[winged tangle]

Like the whole pdf?

[opaque pagoda]

Okay, I’m looking at the notes you’ve written on the left, and I’ve just figured something out: yes, those first five bullets points are the five axioms of Young’s Geometry.

Yes, please!

[winged tangle]

only in Euclid space we also learnt young and fanos

Fanos

[opaque pagoda]

I thought so! Please provide the pdf so I can sift through it!

Do you happen to know where bullets 6-9 originate from? There are only 5 axioms, so I want to know where you pulled the last four pieces of information from.

[sonic wren]

shortypaw has been timed out for 5m
Reason: Images/Videos Spam

shortypaw | 1090145310229139456

[opaque pagoda]

Hm. I’m guessing that the last four are just reiterations of the previously stated axioms. Let’s move on then.

[opaque pagoda]

It is not required, but I’d like to see the proof and justification for each step you’ve taken. This illustration of yours is wildly different from the one I have constructed.

[winged tangle]

Sorry I got muted

Because I sent the pics it count as spam

[winged tangle]

Yes it’s repetition of the axioms

That is how she taught us

[winged tangle]

So the way I did the proof is basically we write the axiom and then we do the diagram

[opaque pagoda]

Oh, I see! So the diagram is already given! What an interesting way of drawing it!

[winged tangle]

No it’s like this is the answers but I didn’t look at it I promise I did it myself

[opaque pagoda]

Generally, I was expecting you to draw it like this, but I don’t know how your teacher teaches!

If you did it yourself, and it’s the same as the answer key, then it’s correct!

[winged tangle]

I promise I did it myself and in her text book it’s similar

[winged tangle]

I don’t know it this way

[opaque pagoda]

Here was my attempt, if you were curious:

[winged tangle]

Woahhhh

That is so pretty

[opaque pagoda]

Well, I have yet to see a diagram that looks like the one your teacher provided, but…different instructors teach things in different ways, so…

[winged tangle]

This was mine

[opaque pagoda]

Either way, if you have no further inquiries, then I think you’re good to go!

[winged tangle]

And this was hers

[opaque pagoda]

It’s harder when the prof. Makes their own interpretation of these things…let me check it real quick.

[winged tangle]

Sure

[winged tangle]

It’s page 18 I sent in the pictures

[opaque pagoda]

Why does it say "...13 lines" at the very end of the proof? We're supposed to be proving that there can only be 12 lines, aren't we?

[winged tangle]

It says at least so it can be more

Like we can find more

[opaque pagoda]

Oh, okay. Back to examining then.

[winged tangle]

yes

please thank youuu

[opaque pagoda]

L1: The diagonal, correct? Why does it look like L1 and L12 are being labeled at the same line?
L2: the vertical? If so, then yes.
L3: the horizontal? Then yes.
L4: Horizontal? Then yes.
L5: Vertical? Yes.
L6: Yes if it’s vertical
L7: It gets tricky right here. Hm.
L8: The vertical which stretches throughout the entire shape? Then yes. But then you also have that labeled as L11?
I’m confused on Line 1, 7, 8, 9, 11, 12. Why do I see lines 7 & 8 being labeled twice? Explain your thought process.

[winged tangle]

Sure I will use some highlights and show them to you

[opaque pagoda]

Much obliged.

I find that color coding this theorem is the easiest way when it comes to examining, or, writing down that last sentence like your prof. did.

But then again, you should probably not use anything besides a black pen or a pencil if you’re drawing this for an exam/assignment

[winged tangle]

Yes for my exam I’m only allowed to use a pen

[winged tangle]

Is it complicated if not I will try to make it more clair

[opaque pagoda]

Ah, okay, I see now!

Okay, you're not allowed to do that. Look at Line 12. In the middle, when the line breaks, and changes direction--that's a completely different line.

What would be correct would be if you labeled the blue and the orange as line 12. Does that make sense?

One more thing I noticed: in the answer key, your teacher noted that Line M and RP were two separate lines. I don't know about you, but those look like the same line to me.

If I counted correctly, it looks like there are fourteen separate lines in your illustration.

[opaque pagoda]

I don't know if your inference was correct or not; I'm not sure if you can draw more than 12 lines in order to recieve full credit for the question!

So, if we're going by the teacher's implied grading, I would most likely mark this answer only partially correct.

Is there something you notice about the inner lines in her answer key, that you have failed to recreate? If you answer this question correctly, you'll be able to see your errors!

[winged tangle]

Um

Like I made a mistake

[winged tangle]

Well I mean mine is not the exact shape like hers but like I still made 9 point with 12 lines won’t that count?

[opaque pagoda]

Okay, so here’s the problem: the theorem that your teacher mashed was originally taken from Young’s theorem 9, which states word for word: “There are EXACTLY 12 lines in the geometry.” NOT 11, NOT 13—make no mistake of that, but TWELVE.

So, I think this is a question that needs to be further answered by your teacher, but my interpretation is this: there should only be 12 lines. No more, and no less.

[winged tangle]

I proved that in young system and I got it correctly

I can send it if you want to see it

[opaque pagoda]

Go ahead.

[winged tangle]

It looks a bit weird I’m sorry

[opaque pagoda]

Messy, but beautiful!

I have to admit that I cannot read this without great difficulty, but if your teacher marked this with full points, and this is exactly like what you drew in the previous photo, then I think you’re good to go!

[winged tangle]

I did it the exact way she did in the lecture

[winged tangle]

Thank you poli again you helped me a lot today I will try my best to get full mark next Wednesday

[opaque pagoda]

This may be untactful, but I quite despise the way your teacher has drawn out this diagram. But yes, then just follow your teacher’s rubric.

Of course! I’m always happy to help! I hope you get full marks on your exam! Drop any other questions before then, if you have any doubts!

[winged tangle]

I’m sorry I will be a bother until my exam

[opaque pagoda]

Nihil est! I am happy to be bothered!

[winged tangle]

I will tell you if I have a question tomorrow if you could answer me please if you had time

[winged tangle]

thank you so much you are the smartest man ever

[cerulean wing]

@winged tangle

:HelpIcon:| Help Reminder

Hello shortypaw, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

@opaque pagoda @indigo marsh @coral carbon @ember quest @sonic swift @dapper matrix The user still needs help with this help request.

[winged tangle]

no

NO

PLEASE IM SORRY

[dapper matrix]

Hm?

[winged tangle]

I meant I WANAN keep the thread open

PLEASE IM SO SORRY GUYS

[coral carbon]

It's fine, don't panic

[winged tangle]

I AM

[coral carbon]

next time you can just send a "bump" in here without pressing the button

it's fine, you didn't know

[dapper matrix]

Oh, Rion || #helper-mod-chat ||, I'm having a bit of an issue.

[winged tangle]

I will I promise I’m so sorry guys

[winged tangle]

Thank you so much rion for understanding me