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.

Answer:
:
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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