Question

In the given figure, AD is bisector of $\angle$A and AB$=$AC. Then $\Delta$ACD, $\Delta$ABD are congruent by which criterion?

• A. AAA
• B. SAS
• C. ASA
• D. Both (B) and (C)

Answer 1

The correct option is D Both (B) and (C)

In the given figure, If $AD$ is the bisector of $\angle A$, then

$\angle BAD=\angle CAD\Rightarrow BD=CD$

And It is given, that $AB=AC$

$\therefore \angle B=\angle C$

Therefore $△ABD$ and $△ACD$ are congruent by $ASA$ and $SAS$