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ASA Criteria for Congruency of Triangles

STR is an iso...

Question

$△$ STR is an isosceles triangle where ST=TR
Also PT = TR,
and $∠$ TSP = $∠$ TRQ
Find the angle of $△$ PST that corresponds to $∠$ RQT of $△$ RQT.

∠

PST

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∠

STP

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∠

TPS

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Cannot be determined

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Solution

The correct option is A $∠$ PST
In $△$ PTS and $△$ QTR
$∠$ TSP = $∠$ TRQ (given)
ST = TR (given)
$∠$ PTS = $∠$ QTR (vertically opposite angles)

Hence $△$ PTS $≅$ $△$ QTS by ASA criterion for congruency of triangles

Hence the angle of $△$ PST that corresponds to $∠$ RQT of $△$ RQT is $∠$ PST

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Similar questions

$\frac{P S}{S Q}$ = $\frac{P T}{T R}$ and $∠$ PST = $∠$ PRQ. Prove that $Δ$ PQR is an isosceles triangle.

△

∠

∠

^{\circ}

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

∠ P S T = ∠ P R Q

△ P Q R

△

≅

△

△

△

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

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