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Math Help - Difficult Triangle Proof

  1. #1
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    Difficult Triangle Proof

    AD, BE, CF are altitudes of ∆ABC. Prove what these same segments are in ∆DEF.
    Difficult Triangle Proof-abc.png
    My guess is they are angle bisectors. I can not prove this however. I have been trying to prove it with similar and congruent triangles however I have not been able to get anywhere significant.

    Thanks in advance
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  2. #2
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    Difficult Triangle Proof-angle-bisectors.pdf
    Quote Originally Posted by MATNTRNG View Post
    AD, BE, CF are altitudes of ∆ABC. Prove what these same segments are in ∆DEF.
    Click image for larger version. 

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    My guess is they are angle bisectors. I can not prove this however. I have been trying to prove it with similar and congruent triangles however I have not been able to get anywhere significant.

    Thanks in advance
    Yes, they are bisectors.
    Attached is one way to show this for equilateral, isosceles and scalene triangles.
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