Question

In the figure given below PQR is a triangle in which , PL is the bisector of $\angle QPR.$. If $PL\perp QR,$ show that $\Delta PQR$ is isosceles.

Answer 1

$PL$ is the bisector of $\angle QPR\Rightarrow \angle 1=\angle 2$

$PL\perp QR\Rightarrow \angle PLQ=\angle PLR={90}^o$

Now in $△PQL$ and $△PRL$

$\angle 1=\angle 2$ [Given]

$PL$ [Common side]

$\angle PLQ=\angle PLR={90}^o$

$\therefore$ By As A, $PQL$ $△PRL$

$\therefore \angle Q=\angle R[C.P.C.T]$

$\Rightarrow PQ=PR$

$\Rightarrow △PQR$ is isosceles