Question

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

• A. isosceles
• B. equilateral
• C. right angled
• D. scalene

Answer 1

The correct option is A isosceles

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.