Question

In the given figure, $AB=AC$.

Then $AD$ does not bisects angle $A$.

• A. True
• B. False

Answer 1

The correct option is B False

In triangle ABC, since AB = AC
thus, $\angle ABC=\angle ACB$ (I) (angles opposite to equal sides are equal)
Now, in triangles DPB and DQC
$\angle P=\angle Q=90$ (Given)
$\angle ABC=\angle ACB$ (From I)
$BD=DC$ (Given)
Thus triangles, $DPB\cong DQC$ (ASA Congruency)
Hence, $DP=DQ$
Join AD.
In $△$s ADP and ADQ
$AD=AD$ (common)
$DP=DQ$ (Proved above)
$\angle P=\angle Q=90$(Given)
Thus, $ADP\cong ADQ$ (SSA congruency)
Hence, $\angle PAD=\angle QAD$. We can say, AD bisects $\angle A$