Question

Pls solve the question..

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Answer 1

Answer:

Step-by-step explanation:

Given: Ray PR || ray QS

Ray PR and ray QS are the bisectors of ∠BPQ and ∠PQC respectively.

To prove: line AB || line CD

Proof:  Ray PR || ray QS and seg PQ is their transversal.

∠RPQ = ∠SQP ….(i) [Alternate angles]  

∠RPQ = (1/2) ∠BPQ …. (ii) [Ray PR bisects ∠BPQ]

∠SQP = (1/2) ∠PQC [Ray QS bisects ∠PQC]  

∴ (1/2) ∠BPQ = (1/2) ∠PQC

∴ ∠BPQ = ∠PQC

But, ∠BPQ and ∠PQC are alternate angles on lines AB and CD when line EF is the transversal.

∴ line AB || line CD [Alternate angles test]