Question

State whether it is true/false:

In the given figure, $AB=AC$, then $DP=DQ$.

• A. True
• B. False

Answer 1

The correct option is A True

In triangle ABC, since AB = AC

thus, $\angle ABC=\angle ACB$ .......(1) (angles opposite to equal sides are equal)

Now, in triangles DPB and DQC

$\angle P=\angle Q=90$ (Given)

$BD=DC$ (Given)

$\angle ABC=\angle ACB$............... (From 1)
Thus triangles, $DPB\cong DQC$ (RHS Congruency)
Hence, $DP=DQ$