#Trapezoid

51 messages · Page 1 of 1 (latest)

shy swift
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In the diagram, ABCD is an isosceles trapezoid, where AB∥CD.
It is given that ∠BAC=60∘, AC=17 cm, and CP∥BD.

Fill in the blanks so that the statements are correct.
A) The triangle △APC, based on its sides, is ___________.
B) The measure of ∠AOD is ___________.
C) The midsegment of the trapezoid is ___________ cm.

So far i've found out that APC is equilateral triangle, and that angle AOD = 120

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scenic jewelBOT
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shy swift
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And also that DB=CP=CA=AP=17

karmic pike
shy swift
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isn't angle AOD=120?

karmic pike
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Yes, 120°. How did you prove that?

shy swift
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since triangle AOB is also equilateral, angle COD is also 60, and we are left with 240 for the last two angles to form 360, so 240/2=120 for each angle AOD and BOC

karmic pike
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Nice!

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Now, (C)... Hm.

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Can't say I immediately see how to do it.

shy swift
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really? is it that simple?

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i feel like it's in front of my eyes and i just can't see it

karmic pike
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But, I can see it now.

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Here's a hint: let AC = x, CD = t. Then what is AB?

shy swift
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AB= 17-BP, but i don't think you are asking me that xd

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oh

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and BP=CD

karmic pike
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Right.

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So, AB = x - t, right?

shy swift
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Yes

karmic pike
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Now, suppose the midline has length l.
If we know the bases AB and CD, how can we find l?

shy swift
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l=(AB+CD)/2 ?

karmic pike
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Right.

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And since in our case AB = x - t and CD = t, what would l be in terms of those?

shy swift
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l=x/2?

karmic pike
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Right.

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And what are we given?

shy swift
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that AC=17?

karmic pike
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Yeah. And we denoted it by x.

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So, there you go.

shy swift
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oh

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so it's 8.5

karmic pike
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We don't even need the individual lengths of bases.

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Yeah. Don't forget about units, though.

shy swift
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how did you learn to spot these things so fast, i draw the height of the trapezoid, found all angles, saw which sides are equal and wasn't able to see anything that can help me

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now that you told me it's obvious and so simple, but up to now it was like i was just blind

karmic pike
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To be honest, I'm not that good at geometry, as I haven't directly used it in some time.

shy swift
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do you have any other suggestions? Like maybe books or courses? How should i know when i need to search for help or keep trying to solve it

karmic pike
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Don't really know.

shy swift
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i've had cases when i was trying to solve something simple as that for days before asking for help, which slows down the whole process

karmic pike
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This is school material, and I don't quite remember how I approached it.

karmic pike
shy swift
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ah, i see

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thank you so much for the help! I often find you in the chat when i've posted a question, thank you for being such an active helper

karmic pike
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You're welcome!

shy swift
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+close

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# shy swift +close
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