ABC is an isosceles triangle in which AB=AC.Also,D is a point such that BD=CD. prove that AD bisects angle A and angle D.
In triangle abc ad is the median now in triangle abd and triangle acd ab=ac (given) bd=cd(given) & ad=ad (common). So by sss congruence criterion, triangle ABD is congruent to triangle ACD. So angle bad is equal to angle cad and angle BDA is equal to angle CDA by cpct. Now since Angle bad = angle cad and angle bda = angle cda. Implies ad bisects angle A and angle D