In the above figure- TQ - SR and - TQP - SRQ-If- - RQS -55- then- - QPT - -A- 759B- 65-C- 45-D- 55-

The correct option is D 55°Consider TPQ and SRQ, ∠PTQ = ∠QSR = 90° nbsp; TS = nbsp; SR (given) ∠TQP = ∠SRQ (given) Hence, TQP ≅SRQ by ASA criterion for co ...

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Standard VII

Mathematics

ASA Criteria for Congruency of Triangles

In the above ...

Question

In the above figure, TQ = SR and $∠$ TQP = $∠$ SRQ.
If, $∠$ RQS = 55°, then, $∠$ QPT = ?.

55°

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45°

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65°

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75°

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Solution

The correct option is A 55°
Consider $△$ TPQ and $△$ SRQ,
$∠$ PTQ = $∠$ QSR = 90°
TS = SR (given)
$∠$ TQP = $∠$ SRQ (given)

Hence, $△$ TQP $≅ △$ SRQ by ASA criterion for congruency of triangles

$∴$ $∠$ QPT = $∠$ RQS = 55° ...corresponding parts of the congruent triangles

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Question 23

In the given figure, PQ = PR, RS = RQ and $S T ∥ Q R$ . If the exterior $∠ R P U$ is $140^{\circ}$ , then the measure of $∠ T S R$ is

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In the above figure, TQ = SR and ∠TQP = ∠SRQ. If, ∠RQS = 55°, then, ∠QPT = ?.

The correct option is A 55°Consider △TPQ and △SRQ, ∠PTQ = ∠QSR = 90° TS = SR (given) ∠TQP = ∠SRQ (given) Hence, △TQP ≅△SRQ by ASA criterion for congruency of triangles ∴ ∠QPT = ∠RQS = 55° ...corresponding parts of the congruent triangles

In the above figure, TQ = SR and $∠$ TQP = $∠$ SRQ.
If, $∠$ RQS = 55°, then, $∠$ QPT = ?.