Question

In triangle $ABC$, bisector of angle $BAC$ meets opposite side $BC$ at point $D$. If $BD=CD$, then $△ABC$ is isosceles.

• A. True
• B. False

Answer 1

The correct option is A True

In $△ABD$ and $△ACD$,
$BD=CD$ (Given)
$AD=AD$ (Common)
$\angle BAD=\angle CAD$ (Given)
thus, $△ABD\cong △ACD$ (SAS postulate)
Thus, $AB=AC$ (By cpct)
Hence, ABC is an Isosceles triangle.