Thread: Difficult Triangle Proof

AD, BE, CF are altitudes of ∆ABC. Prove what these same segments are in ∆DEF.

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

Originally Posted by MATNTRNG

AD, BE, CF are altitudes of ∆ABC. Prove what these same segments are in ∆DEF.

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.