Question

In the given figure ∠R = ∠S and ∠RPQ = ∠PQS. Prove that ∆PQS ≅ ∆RQP and hence prove that SP= QR




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Answer 1

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Answer 2

Answer:

In the kite shown, PQ = PS and ∠QPR = ∠SPR.

(i) Find the third pair of corresponding parts to make ∆ PQR ≅ ∆PSR by SAS congruence condition.

(ii) Is ∠QRP = ∠SRP?

Solution:

(i) In ∆ PQR and ∆ PSR

PQ = PS                        →        given

∠QPR = ∠SPR                 →         given

PR = PR                        →         common

Therefore, ∆PQR ≅ ∆PSR by SAS congruence condition

(ii) Yes, ∠QRP = ∠SRP (corresponding parts of  congruence triangle).

Step-by-step explanation: