Question

State true or false:

From the given figure we can say that,

$AB=AC$.

• A. True
• B. False

Answer 1

The correct option is A True

In $△APQ$,
$AP=AQ$
thus, $\angle APQ=\angle AQP=x$ (Angles opposite to equal sides are equal)
$\angle APQ+\angle APB=180$
$x+\angle APB=180$
Thus, $\angle APB=180-x$
Similarly, $\angle AQC=180-x$
Thus, $\angle APB=\angle AQC$...(I)
Now, In $△$s APB and AQC
$AP=AQ$ (Given)
$\angle APB=\angle AQC$ (From I)
$\angle BAP=\angle QAC$ (Given)
Thus, $△APB\cong △AQC$ (ASA Congruency)
or $AB=AC$