A transversal EF of line AB and line CD intersects the line at point P and Q respectively. Ray PR and ray QS are parallel and bisectors of angle BPQ and angle PQC respectively.
Prove that line AB ll line CD.
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as angle SPQ =angle QPR (alternate angles)
and also ray SQ and rayRP bisect angle CQP and angleBPQ
So 2×angle SQP=2×angleRPQ so angle CQP=angle BPQ then CD//AB.
and also ray SQ and rayRP bisect angle CQP and angleBPQ
So 2×angle SQP=2×angleRPQ so angle CQP=angle BPQ then CD//AB.
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angle SQP = angle QPR (alternate angles)
Ray SQ and Ray RP bisect angle CQP and angle BPQ (given)
2×angle CQR = 2×angle BPQ
angle CQR = angle BPQ
Ifa pair of alternate angles formed by a transversal of two lines is congruent then the two lines are parallel (by alternate angle test)
therefore, line AB is parallel to line CD
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