In the figure given below, two parallelograms ABCD and PQCD lie on the same base CD and between the same parallel lines AQ and CD. Then, $△ A P D$ and $△ B Q C$ are congruent

True

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False

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Solution

The correct option is A True
We know parallelograms on the same base and between the same parallels are equalin area.
Thus, Area //gm DABC = Area //gm DPQC
Area $△ A P D$ + Area trapezium DPBQ = Area trapezium DPBQ + Area $△ A P D$
Area $△ A P D$ = Area $△ A P D$

Also AP + PB = PB + BQ
Thus, AP = BQ

Also, AD = BC and DP = CQ ... (opposite sides of a parallelogram)

$△ A P D ≅ △ B Q C$ ....(by SSS criterion)

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In the figure given below, two parallelograms ABCD and PQCD lie on the same base CD and between the same parallel lines AQ and CD. Then, $△ A P D$ and $△ B Q C$ are congruent

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In the figure given below, two parallelograms ABCD and PQCD lie on the same base CD and between the same parallel lines AQ and CD. Then, △APD and △BQC are congruent

In the figure given below, two parallelograms ABCD and PQCD lie on the same base CD and between the same parallel lines AQ and CD. Then, $△ A P D$ and $△ B Q C$ are congruent