In the figure shown below - if PS-SQ- PT-TR and-PST- -PRQ- then find the type of -PQR -3 Marks-

It is given that PS/SQ = PT/TR So, ST || QR[1 Mark] ∴ nbsp;∠PST=∠PQR (Corresponding Angles) Also, it is given that ∠PST = ∠PRQ So, ∠PRQ = nbsp; nbsp ...

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

Byju's Answer

Standard IX

Mathematics

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 find the type of $Δ$ PQR . $[3 M a r k s]$

Open in App

Solution

It is given that

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

So, ST || QR $[1 M a r k]$

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

Also, it is given that

$∠$ PST = $∠$ PRQ

So, $∠$ PRQ = $∠$ PQR $[1 M a r k]$

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

i.e., $Δ$ PQR is an isosceles triangle. $[1 M a r k]$

Suggest Corrections

Similar questions

Q. In below shown figure,

\frac{P S}{S Q}

\frac{P T}{T R}

and

∠

PST =

∠

PRQ. Then what type of triangle is

Δ

PQR.

(3 Marks)

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

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

In below shown figure, $\frac{P S}{S Q} = \frac{P T}{T R}$ and $∠ P S T = ∠ P R Q$ . 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 find the type of ΔPQR . [3 Marks]

It is given that PSSQ = PTTR So, ST || QR [1 Mark] ∴ ∠PST=∠PQR (Corresponding Angles) Also, it is given that ∠PST = ∠PRQ So, ∠PRQ = ∠PQR [1 Mark] ∴ PQ = PR (Sides opposite to equal angles) i.e., ΔPQR is an isosceles triangle. [1 Mark]

In the figure shown below , if $\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST= $∠$ PRQ, then find the type of $Δ$ PQR . $[3 M a r k s]$