Question

prove that he line joining the point of intersection of two angular bisectors of the base angle of an isosceles triangle to the vertex bisects the vertical angle.

Answer 1

Answer:

Let ABC be an isosceles triangle such that AB=AC.

Let AD be the bisector of ∠A.

To prove:- BD=DC

Proof:-

In △ABD&△ACD

AB=AC(∵△ABC is an isosceles triangle)

∠BAD=∠CAD(∵AD is the bisector of ∠A)

AD=AD(Common)

By S.A.S.-

△ABD≅△ACD

By corresponding parts of congruent triangles-

⇒BD=DC

Hence proved that the perpendicular drawn from the vertex angle to the base bisect the vertex angle and base.