Question

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Answer 1

Answer:

∆PQR and ∆RSP,

∠RPQ = ∠PRS (Since, SR ∥ PQ),

∠QRP = ∠SPR (Since, PS ∥ QR),

PR = PR

Therefore, ∆PQR ≅ ∆RSP, (By AAS criterion of congruency)

Therefore, QR = PS (CPCTC).

In ∆PQR and ∆QPS,

QR = PS

PR = QS (Given),

PQ = PQ.

Therefore, ∆PQR ≅ ∆QPS (By SSS criterion of congruency)

∠PQR = ∠QPS (CPCTC).

But ∠PQR + ∠QPS = 180° (Since, QR ∥ PS)

Therefore, ∠PQR = ∠QPS = 90° (Proved)

Step-by-step explanation:

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