Question

Prove it . The line, joining the mid-point of the base of an isosceles triangle and the opposite vertex, is perpendicular to the base and bisects the angle at the vertex.​

Answer 1

Answer:

$\ {Answer}$

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.