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

Let ABC be a triangle such that AD is the angular bisector of exterior vertical angle, ∠EAC and AD ∥ BC.

From figure, 

∠1 = ∠2 [AD is a bisector of ∠ EAC] 

∠1 = ∠3 [Corresponding angles] 

and ∠2 = ∠4 [alternative angle] 

From above, we have ∠3 = ∠4 

This implies, AB = AC 

Two sides AB and AC are equal. 

Δ ABC is an isosceles triangle.