Question

ABC is an isosceles triange in which AB=AC.Also D is a point such that BD=CD.Prove that AD bisects ang.A and ang.D

Answer 1

Given- AB=AC and BD=CD
prove-AD bisect ang. A and D
or, ang 1=2
ang. 3=4

proof- Consider∆BAD and ∆CAD
AB=AC (given)
BD=CD (given)
AD=AD(coman)
∆BAD=∆CAD (by S.S.S rule)
so, ang.1=2 (byCPCT)
ang. 3=4
hence proved