Question

In the given figure, $AD$ is the angle bisector and perpendicular bisector to $BC$, then $△$ $ABC$ must be

• A. Equilateral triangle
• B. Isosceles triangle
• C. Scalene triangle
• D. Obtuse angled triangle

Answer 1

The correct option is B Isosceles triangle

Taking $△$ $ABD$ and $△$ $ACD$
$\angle BAD=\angle CAD$ ( $\because AD$ is the angle bisector)

$\angle$ $ADB=$ $\angle$ $ADC$ ( $\because AD\perp BC)$

$BD=CD$ ($\because AD$ is perpendicular bisector to BC)

Hence, Using AAS rule$△ABD\cong △ACD$

We know corresponding sides of congruent triangles are equal, hence $AB=AC$
As two sides of $△$ $ABC$ are equal so $△$ $ABC$ is Isosceles triangle.