Question

In the figure shown below , if $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and$\angle$PST= $\angle$PRQ, then $\Delta$PQR is _______ triangle.

Answer 1

It is given that

$\frac{PS}{SQ}$ = $\frac{PT}{TR}$

So, ST || QR

$\therefore$ $\angle$PST=$\angle$PQR (Corresponding Angles)

Also, it is given that

$\angle$PST = $\angle$PRQ

So, $\angle$PRQ = $\angle$PQR

$\therefore$ PQ = PR (Sides opposite to equal angles)

i.e., $\Delta$PQR is an isosceles triangle.