# Inscribing a square in a tri

• Oct 6th 2006, 04:55 PM
sarahh
Inscribing a square in a tri
Hi everyone,

I have the following problem to solve: it requires a square to be inscribed in a triangle. Now, the solution is found here but what I need now is to prove two triangles similar. I'm having trouble doing this. Can anyone show me a proof? Thanks in advance.

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sarahh
• Oct 7th 2006, 06:34 AM
CaptainBlack
Quote:

Originally Posted by sarahh
Hi everyone,

I have the following problem to solve: it requires a square to be inscribed in a triangle. Now, the solution is found here but what I need now is to prove two triangles similar. I'm having trouble doing this. Can anyone show me a proof? Thanks in advance.

Math Forum - Ask Dr. Math

sarahh

I expect you wish to prove the triangles AGD and AHK are similar and
also that triangles AGF and AHI are also similar in the attached figure.

As lines HK and GD are parallel (by construction), angles HKA and GDA are
congruent. Also angle DAG is common to both triangles all of the angles in
AGD are congruent to the corresponding angles in AHK, and so these
triangles are similar.

Now look at angles HIA and GFA, these are both right angles (by
construction), and angle HAI is common to both triangles AGF and AHI
so these two triangles have two equal angles, hence all the corresponding
angles are congruent, and so the triangles are similar.

RonL
• Oct 7th 2006, 11:39 AM
sarahh
Thanks captain! I got it!! Also, the last part of the question is to form the ratio AH/AG. How do I conclude/calculate the ratio?

Sarah
• Oct 7th 2006, 01:08 PM
CaptainBlack
Quote:

Originally Posted by sarahh
Thanks captain! I got it!! Also, the last part of the question is to form the ratio AH/AG. How do I conclude/calculate the ratio?

Sarah

I don't quite see how to approach finding this ratio, it is of course the same
as the ratio of any corresponding segments of figures ADGFE, and AKHIJ as
these are similar.

RonL