Question

In below shown figure, $\frac{PS}{SQ}$= $\frac{PT}{TR}$ and $\angle$PST = $\angle$PRQ. Then what type of triangle is $\Delta$PQR.

(3 Marks)

Answer 1

It is given that

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

So, ST || QR [By converse of Basic Proportionality Theorem] (1 Mark)

$\therefore \angle PST=\angle PQR$
(Corresponding Angles) (1 Mark)

Also, it is given that

$\angle$PST = $\angle$PRQ

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

Therefore, PQ = PR (Sides opposite the equal angles)

i.e., $\Delta$PQR is an isosceles triangle. (1 Mark)