CBSE Class 9 Answered

Let ABCD and EFCD be two parallelograms lying on the same base CD and between the same parallels AF and CD.

We have to prove that area of the parallelograms ABCD and EFCD are equal.

In ADE and BCF,

DAE = CBF (Corresponding angles)

AED = BFC (Corresponding angles)

AD = BC (Opposite sides of the parallelogram ABCD)

ADE BCF (By ASA congruence rule)

We know that congruent figures have the same area.

area (ADE) = area (BCF) … (1)

Now, we have:

area (ABCD) = area(ADE) + area (EDCB)

= area (BCF) + area (EDCB) [Using (1)]

= area (EDCF)

Thus, the areas of the two parallelograms ABCD and EFCD are the same.