In the given figure- PS - SQ - PT - TR and - PST - PRQ- then - PQR istriangle-A- an IsoscelesB- a Right angledC- a ScaleneD- an Equilateral

The correct option is A an Isosceles It is given that PS/SQ = PT/TR By converse of Basic Proportionality Theorem (BPT), ST||QR ∴, ∠PST=∠PQR ..........(Corre ...

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Standard IX

Mathematics

In the given ...

Question

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

an Isosceles

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a Scalene

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an Equilateral

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a Right angled

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Solution

The correct option is A
an Isosceles

It is given that

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

By converse of Basic Proportionality Theorem (BPT), 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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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 $Δ P Q R$ is a/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.

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

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Standard IX Mathematics

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In the given figure, PSSQ= PTTR and∠PST= ∠PRQ, then ΔPQR is _______triangle.

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