Question

In the given figure, $AB=AC$. Then, we can say that $AP=AQ$
If this statement is True then enter 1 or enter 0 if False.

Answer 1

Given, $AB=AC$
$\angle ABC=\angle ACB$ ...(Isosceles triangle property)
Now, in $△DPB$ and $△DQC$,

$BD=DC$ ...(Given)
$\angle DBP=\angle DCQ$ ...(Proved above)
$\angle DPB=\angle DQC$ ...(Each ${90}^{\circ }$)

thus, $△DPB\cong △DQC$ ...(ASA postulate)

Hence, $PB=QC$ ...(By cpct)

We know, $AB=AC$

Hence, $AB-PB=AC-QC$
$\therefore AP=AQ$