In the figure shown below- if PS - SQ - PT - TR and - PST - PRQ- then - PQR istriangle-A- ScaleneB- Equilateral triangleC- Right angled triangleD- Isosceles

The correct option is D Isosceles It is given that PS/SQ = PT/TR So, ST || QR ∴ nbsp;∠PST=∠PQR (Corresponding Angles) Also, it is given that ∠PST = ∠PRQ So, ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard X

Mathematics

Converse of Basic Proportionality Theorem

In the figure...

Question

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

Isosceles

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Scalene

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Equilateral triangle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right angled triangle

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A Isosceles
It is given that

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

So, ST || QR

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

Also, it is given that

$∠$ PST = $∠$ PRQ

So, $∠$ PRQ = $∠$ PQR

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

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

Suggest Corrections

Similar questions

In the given figure, $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ, then $Δ$ PQR is _______triangle.

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

Join BYJU'S Learning Program

In the figure shown below , if PSSQ= PTTR and∠PST= ∠PRQ, then ΔPQR is _______ triangle.

The correct option is A IsoscelesIt is given that PSSQ = PTTR So, ST || QR ∴ ∠PST=∠PQR (Corresponding Angles) Also, it is given that ∠PST = ∠PRQ So, ∠PRQ = ∠PQR ∴ PQ = PR (Sides opposite to equal angles) i.e., ΔPQR is an isosceles triangle.

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