Question

Prove that in an isosceles triangle the perpendicular drawn from the vertex angle to the base bisect the vertex angle and the base.

Answer 1

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

Let AD be the bisector of $\angle A$.

To prove:- $BD=DC$

Proof:-

In $△ABD\&△ACD$

$AB=AC(\because △ABC\text{is an isosceles triangle})$

$\angle BAD=\angle CAD(\because \text{AD is the bisector of}\angle A)$

$AD=AD\left(\text{Common}\right)$

By S.A.S.-

$△ABD\cong △ACD$

By corresponding parts of congruent triangles-

$\Rightarrow BD=DC$

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