In the figure shown below- if PS - SQ - PT - TR and - PST - PRQ- then - PQR is a - an triangle-A- isoscelesB- equilateralC- right angledD- scalene

The correct option is A isoscelesIt is given that PS/SQ = PT/TR So, ST || QR ∴∠ PST= ∠ PQR (corresponding Angles) Also, it is given that ∠ PST = nbsp; ∠ PRQ S ...

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Byju's Answer

Standard X

Mathematics

Intercept 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 a/an triangle.

isosceles

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equilateral

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right angled

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scalene

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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

$∴ ∠ P S T = ∠ P Q R$ (corresponding Angles)

Also, it is given that

$∠ P S T = ∠ P R Q$

So, $∠ P R Q = ∠ P Q R$

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

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

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