Question

State the whether given statement is true or false

Prove that a triangle $ABC$ is isosceles, if
(i) altitude $AD$ bisects angle $\angle BAC$, or
(ii) bisector of angle $BAC$ is perpendicular to base $BC$

• A. True
• B. False

Answer 1

The correct option is A True

R.E.F image

Given :- $\angle BAM=\angle CAM$

In $△AMB$ & $△AMC$

$\angle ABC+\angle AMB+\angle BAM={180}^{\circ }=+\angle AMC+\angle CAM+\angle ACB$

$\angle BAM=\angle CAM$

$\angle AMB=\angle AMC={90}^{\circ }$

$\therefore \angle ABC=\angle ACB$

$\therefore AB=AC$ (opposites sides of equal angles are equal)

$\therefore △ABC$ is isosceles triangle