In below shown figure, P S S Q = P T T R and ∠ PST= ∠ PRQ. Then Δ PQR is a/an __ triangle. Options:

In below shown figure, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is a/an _

Question

In below shown figure, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ. Then $Δ$ PQR is a/an __ triangle.

Options:

Answer: Option A
:

It is given that

$\frac{P S}{S Q}$ = $\frac{P T}{T R}$

So, ST||QR [By converse of Basic Proportionality Theorem]

$∴$ , $∠$ PST= $∠$ PQR (Corresponding Angles)

Also, it is given that

$∠$ PST = $∠$ PRQ

So, $∠$ PRQ = $∠$ PQR

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

i.e., $Δ$ PQR is an isosceles triangle.

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