Question

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

Answer 1

Given : In $\Delta ABC,AE\text{is the bisector of vertical exterior}\angle AandAE||BC$

To prove : $\Delta ABC$ Is an isosceles

Proof : $\because AE||BC$

$\therefore \angle 1=\angle B\left(\text{Corresponding angles}\right)\angle 2=\angle C\left(\text{Alternate angle}\right)But\angle 1=\angle 2(\because AE\text{is the bisector of}\angle CAD)\therefore \angle B=\angle C\therefore AB=AC\left(\text{Sides opposite to equal angles}\right)\therefore \Delta ABC\text{is an isosceles triangle}$