$\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST = $∠$ PRQ. Prove that $Δ$ PQR is an isosceles triangle.

Open in App

Solution

It is given that $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ ⋅

So, ST || QR (Theorem)

$∴$ $∠$ PST = $∠$ PQR (Corresponding angles) (1)

Also, it is given that

$∠$ PST = $∠$ PRQ (2)

So, $∠$ PRQ = $∠$ PQR [From (1) and (2)]

$∴$ PQ = PR (Sides opposite the equal angles)

i.e., PQR is an isosceles triangle.

Suggest Corrections

205

Similar questions

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

∠ P S T = ∠ P R Q

△ P Q R

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

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

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

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

Join BYJU'S Learning Program