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Q.

In the given figure, PQ || RS and PQ = RT = SU. Which of the following quadrilaterals have equal area?

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a

PQST and QRTP

b

PQRT and PQSU

c

PQRU and SUPQ

d

PQST and UPQS

answer is B.

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Detailed Solution

It is given that PQ || RS and PQ = RT

∴ PQ || RT and PQ = RT

∴Quadrilateral PQRT is a parallelogram.

[Since, if in a quadrilateral, a pair of opposite sides is equal and parallel, then the quadrilateral is parallelogram]

Similarly, as PQ || SU and PQ = SU, quadrilateral PQSU is a parallelogram.

In the given figure it is seen that parallelograms PQRT and PQSU lie on the same base PQ and between the same parallel PQ and RU.

We know that parallelograms on the same base and between the same parallels are equal in area.

Thus, parallelograms PQRT and PQSU have equal area.

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In the given figure, PQ || RS and PQ = RT = SU. Which of the following quadrilaterals have equal area?