Question

State true or false:

The given figure shows a $\Delta ABC$IN which $AB=AC$ and $BP=CQ$ Then,

$\Delta APQ$ is isosceles

• A. True
• B. False

Answer 1

The correct option is A True

Given, $BP=CQ$
$BP+PQ=CQ+PQ$
$BQ=CP$..(I)
In $△$s, ABQ and ACP,
$AB=AC$ (Given)
$BQ=CP$ (From I)
$\angle ABQ=\angle ACP$ (Isosceles triangle property)
Hence, $△ABQ\cong △ACP$ (SAS postulate)
Hence, $AP=AQ$ (by cpct)
Thus, $△APQ$, is an isosceles triangle.