Theorem 1

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

ABCD and ABEF are two parallelograms on the same base AB and between the same parallels AB, DE

area (ABCD) = area (ABEF)

An alternate way of proving this theorem is as follows:

Since both parallelograms are between the same parallels, they are of equal heights. Also they have equal bases because the base is common; by formula,

area of a parallelogram = base x height

they are of equal areas.

Parallelograms between same parallels and having equal bases are equal. The formula for the area of a parallelogram is proved in the next theorem.