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# Similar Triangles

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I find this problem really hard(they have marked it as a beast problem), and I want to solve it. Can you please help me on this, Thank you. Here is the question:

Oct 9, 2018

#1
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Probably the toughest thing to do here is to find a pair of similar triangles that will be of benefit to you for this particular problem. Try your best to locate similar triangles. Use the given info about the parallel lines to help you.

Oct 9, 2018
#2
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That is the part where I am stuck on because finding the similar triangles is so hard

Oct 9, 2018
#3
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I agree with you. Identifying the similar triangles is the toughest step. I had some trouble myself.

Anyway, we know  $$\overline{AG}\parallel\overline{CH}$$ from the given info. This means that corresponding angles are congruent. Therefore, $$\angle A\cong\angle HCD$$ . Via the reflexive property of congruence, $$\angle HDA\cong\angle HDA$$ . Can you think of two triangles that would be similar knowing this? We are hunting for two triangles that share a vertex at $$\angle HDA$$ . This is the part that I initially overlooked. I hope this hint hel

Oct 9, 2018
#4
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We have  two triangles to consider

First  ...triangle  AGF

Since JE  is a segment drawn parallel to base AG.....we have the following relationship :

FE / JE   = FA / AG

1 / JE  = FA / AG

1/ JE  = 5 /AG

AG = 5  (JE )        (1)

Next...we have triangle AGD

Since  HC  is a segment drawn parallel to  base AG...we have the following relationship :

DC / HC  = DA / AG

1 / HC  =  3 / AG

AG = 3 ( HC )       (2)

Equating (2) and (3)

5 ( JE )  = 3 ( HC )

HC / JE  = 5 / 3

Oct 10, 2018
#5
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Thank you everyone.. It helped a lot XSquaredFactor and CPhill, here is my thought process on this one after XSquaredFactor gave me a hint

Oct 10, 2018
edited by shreyas1  Oct 10, 2018
#6
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Shreyas1,

I think that you have copied this and your other answers off another site.

I have seen no evidence that you even know how to do your own Latex.

I would not be surprised if you do not even know what LaTex is.

Melody  Oct 10, 2018