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Math Help - Inscribing a square in a tri

  1. #1
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    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
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by sarahh View Post
    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
    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
    Attached Thumbnails Attached Thumbnails Inscribing a square in a tri-gash.jpg  
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  3. #3
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    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
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by sarahh View Post
    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
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