# In the figure, PQRS is a parallelogram, and B is the midpoint of side PS.If QP and RB are produced to meet at point A, then prove that AQ=2PQ

1
by sweetriya995

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by sweetriya995

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angleAPB=angleBSR (alternate angles)

PB=BS(given-B is mid pt.)

anglePBA=angleSBR(vertiacally opp. angles)

triangleAPB and tri. BRQ are congruent by ASA.

=>AP=SR (by cpct)__(1)

PQRS is a parallelogram,

=>PQ=SR (opp. sides of a parallelogram are equal)__(2)

according to eq. (1) and (2)

AP=SR

PQ=SR

=>AP=PQ.

AP+PQ=AQ

PQ+PQ=AQ (AP=PQ)

2PQ=AQ

hence proved!