Question

From the given figure it is stated that $AB=AC.$
State true or false.

• A. True
• B. False

Answer 1

The correct option is A True

Given: $AP=AQ$

Hence, $\angle APQ=\angle AQP$ (Isosceles triangle property)

$180-\angle APQ=180-\angle AQP$

$\angle APB=\angle AQC$ (I)
Now, In $△ABP$ and $△ACQ$,

$AP=AQ$ (Given)
$\angle APB=\angle AQC$ (From I)
$\angle BAP=\angle QAC$ (Given)

Thus, $△ABP\cong △ACQ$ (ASA postulate)

$\therefore AB=AC$ ...... by cpct