Question

Prove that the bisectors of the base angles of an isosceles triangle are equal.

Answer 1

Here ABC is an isocelous triangle with angle A= angle B
CM and BN are the angle bisectors
So now we observe tri(BMC) and tri(BNC)

1) BC = BC
2) ang(MBC) = ang(NCB)
3) ang(NBC) = ang(MCB)

so by ASA congruency condition the triangles are congruent
and hence
BN = CM
Proved