Q3 of 31 Page 232

P and Q are the mid points of sides AB and DC of parallelogram ABCD respectively. Let’s prove that PBQD is a parallelogram and triangle PBC = parallelogram PBQD.

Given.


P and Q are the mid points of sides AB and DC of parallelogram ABCD


Formula used.


Formula used.


Area of parallelogram = Base × Perpendicular


Area of triangle = × Base × Height



In PBQD


As P and Q are the mid points of sides AB and DC of parallelogram ABCD


PB = QD and PB || QD


∴ PBQD is a parallelogram


In triangle PBC and Parallelogram PBQD


Both are on same base PB which lies on line AB


And AB||CD ∵ Opposite sides of parallelogram are parallel


⇒ Both parallelogram and triangle are on same base and lies between parallel lines AB and CD


∴ triangle PBC = × parallelogram PBQD


Hence proved;


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