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State true or false.

The parallelogram on the same base and between the same parallels are equal in area.

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True

False

answer is A.

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Detailed Solution

Suppose there are two parallelogram such as
ABCD and EFCD in which
CD= same base
CD lie between same parallel which are AF and CD.
Question Image

As opposite sides of parallelogram are parallel. So,

AB ∥ CD

and

ED ∥ FC

Also,

∠ DAB = ∠ CBF

[from Corresponding angles]

∠ DEA = ∠ CFE

[Corresponding angles ]

AD = BC

[parallelogram opposite sides are equal]
Now, in

△ AED and △ BFC

∠ DEA = ∠ CFE

∠ DAB = ∠ CBF

Thus,

AD = BC

So, from angle angle side congruency property of triangle,

△ AED ≅ △ BFC

Thus, in congruent triangle,

ar (△ AED) = ar (△ BFC)

ar (ABCD) = ar (△ ADE) + ar (EBCD)

= ar (△ BFC) + ar (EBCD)

= ar (EBCD)

Thus,

ar (ABCD) = ar (EBCD)

Hence, the given statemnt is true.
Correct option is 1.

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