SOLUTION: Triangle ABC is not isoceles. Prove that altitude BD would not bisect AC.

Algebra ->  Geometry-proofs -> SOLUTION: Triangle ABC is not isoceles. Prove that altitude BD would not bisect AC.      Log On


   

Question 129774: Triangle ABC is not isoceles. Prove that altitude BD would not bisect AC.
Answer by MathLover1(20855) About Me  (Show Source):
You can put this solution on YOUR website!
If you construct the altitude you will see that the sides AB and CB are not+congruent.

I think the way to prove opposite will be best way to shove that altitude BD would not bisect AC.
So, let's assume that the altitude does bisect AC.

Then AD and DC are congruent (by the def. of bisector),
so triangles BAD and BDC are congruent (by the side-angle-side theorem)
if BA and BC are congruent, then ACB is+isosceles

Hence, if the altitude bisects AC, then the triangle must+have+been+isosceles to start with.