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## Question

Which statement proves that PQRS is a parallelogram? The slopes of SP and RQ are both –2 and SP = RQ = . The slopes of RS and QP are both 3 and SP = RQ = . The midpoint of RP is and the slope of RP is . The midpoint of SQ is and SQ = 5

## Answer

Answer:The correct option is 1. The figure PQRS is a parallelogram, if slope of SP and RQ are both –2 and SP = RQ.Step-by-step explanation:The opposite sides of a parallelogram are parallel are equal.In the quadrilateral PQRS,PQ and RS are opposite sides.SP and RQ are opposite sides.The slope of two parallel lines are same.If the slopes of SP and RQ are both –2. It means SP and RQ are parallel. It is also given thatSP = RQSince one pair of opposite sides are equal and parallel, therefore the another set of opposite sides is also parallel and equal.The opposite sides are prallel and equation, so the quadrilateral PQRS is a parallelogram.Thus correct option is 1.

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