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Question
If in a quadrilateral PQRS, PQ = RS and PQ || SR, then ∠SRQ is always equal to
If in a quadrilateral PQRS, PQ = RS and PQ || SR, then ∠SRQ is always equal to
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Solution
The correct option is D ∠SPQ
Given a quadrilateral PQRS such that PQ || SR and PQ = RS.Now, joining QS.
In ΔPQS and ΔRSQ,
PQ = SR (Given)
∠PQS = ∠RSQ (Alternate interior angles)
QS = QS (Common)
∴ΔPQS ≅ ΔRSQ (SAS congruence rule)
⇒ ∠SRQ = ∠SPQ (CPCT)
Hence, the correct answer is option (d).
Given a quadrilateral PQRS such that PQ || SR and PQ = RS.Now, joining QS.
In ΔPQS and ΔRSQ,
PQ = SR (Given)
∠PQS = ∠RSQ (Alternate interior angles)
QS = QS (Common)
∴ΔPQS ≅ ΔRSQ (SAS congruence rule)
⇒ ∠SRQ = ∠SPQ (CPCT)
Hence, the correct answer is option (d).
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