Question

A Transversal ef of line ab and line cd intersects the line at point p and p respective Ray pr a and Ray qs are parallel and bisectors of bpq and pqs respective proves that line ab n line cd
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Answer 1

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]

:)