Abc is a triangle where ad bisects angle a and d is the midpoint of bc prove that triangle is isosceles

Answer 1

In triangles adb and adc,
angle adb = angle adc
bd = dc
ad = ad
So, the triangles are congruent, meaning
ab = ac so abc is isosceles.

Answer 2

I've seen this mistakes in a lot of pages. But you should know S.S.A. axiom doesn't prove triangles are congurent..