Difficult Triangle Proof

Mar 2010
144
2
AD, BE, CF are altitudes of ∆ABC. Prove what these same segments are in ∆DEF.
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
 
Dec 2009
3,120
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View attachment angle bisectors.pdf
AD, BE, CF are altitudes of ∆ABC. Prove what these same segments are in ∆DEF.
View attachment 18204
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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