Question

If the bisector of the exterior vertical angle of a triangle is parallel to the base, show that the triangle is isosceles.

Answer 1

Join A to D

Hence,

$\begin{array}{c}AD\parallel BC\\ \Rightarrow \angle ACB=\angle CAD\left(alternateangle\right)\\ \Rightarrow and\angle BAC=\angle ACD\left(alternateangle\right)\\ \Rightarrow \end{array}$

Hence

AB=AC (by ASA congurency )

so, it is isosceles triangle.