In below shown figure- PS - SQ - PT - TR and - PST - PRQ- Then - PQR is an isosceles Triangle-A- FalseB- True

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

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Byju's Answer

Standard IX

Mathematics

Basic Proportionality Theorem

In below show...

Question

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

Isosceles

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False

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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

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

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

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Q. In the figure shown below , if

\frac{P S}{S Q}

\frac{P T}{T R}

and

∠

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PQR is a/an triangle.

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In below shown figure, PSSQ= PTTR and∠PST= ∠PRQ. Then ΔPQR is an isosceles 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 Therefore, PQ = PR (Sides opposite the equal angles) i.e., ΔPQR is an isosceles 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.