Question

prove that in an isosceles triangle the bisector of non equal angle divides the triangle into 2 congruent triangles.

Answer 1

In an isosceles triangle the bisector of non equal angle divides the triangle into 2 congruent triangles.

Proof

The figure attached with this answer shows an isosceles triangle ABC.

In this triangle ABC, <A=<C, BD is the bisector of non equal <B.

BD divides tha triangle ABC into two triangles, ABD and CBD.

Consider these two triangle,

BD is the bisector of <B ,therefore <ABD = <DBC

AB=AC because ABC is an isosceles triangle.

and  BD = BD(common to both the triangle.

By SAS criteria ABD ≅ CBD