Theorem 2

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The area of a parallelogram is equal to that of a rectangle of the same base and of the same altitude.

ABCD is a parallelogram and ABEF is a rectangle. They have common base AB and same height AF (or BE)

Corollary

Parallelograms having equal bases and equal altitudes are equal in area.

A diagonal bisects a parallelogram. Each triangle has area equal to one half the area of the parallelogram.

The same result is proved in the next theorem.