Question

Pq and rs are two equal and parallel line segments. Any point m not lying on pq or rs is joined to q and s and lines through p parallel to qm and through r parallel to sm meet at n . Prove that line segments mn and pq equal and parallel to each other

Answer 1

Answer:

PQ=RS and MN ║ QM

Angle RPN =  Angle SQM

PR = QS

Δ PRN≅QSM

PN = QM and RN = SM

∵ PN ║ QM and PN = QM

PQMN is a parallelogram

∵RN ║ SM and RN = SM

RNSM is a parallelogram

Thus, PQ = MN and PQ ║ MN

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Step-by-step explanation:

Answer 2

Answer:

PQ=RS and MN ║ QM

Angle RPN =  Angle SQM

PR = QS

Δ PRN≅QSM

PN = QM and RN = SM

∵ PN ║ QM and PN = QM

PQMN is a parallelogram

∵RN ║ SM and RN = SM

RNSM is a parallelogram

Thus, PQ = MN and PQ ║ MN

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