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

Given:

The bisector of the exterior vertical angle of a triangle is parallel to the base.

To do:

We have to show that the triangle is isosceles.

Solution:

Let in $\triangle ABC, AE$ is the bisector of vertical exterior angle $A$ and $AE \parallel BC$

$AE \parallel BC$

This implies,

$\angle 1 = \angle B$             (Corresponding angles)

$\angle 2 = \angle C$                (Alternate angles)

$\angle 1 = \angle 2$              ($AE$ is the bisector of $\angle CAD$)

This implies,

$\angle B = \angle C$

$AB = AC$               (Sides opposite to equal angles are equal)

Therefore, $\triangle ABC$ is an isosceles triangle.

Hence proved.

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Updated on: 10-Oct-2022

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