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| Theorem 1 |
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| Parallelograms on the same base and between the same parallels are equal in area. |
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| ABCD and ABEF are two parallelograms on the same base AB and between the same parallels AB, DE |
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| area (ABCD) = area (ABEF) |
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| An alternate way of proving this theorem is as follows: |
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| 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, |
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| area of a parallelogram = base x height |
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 they are of equal areas. |
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| Parallelograms between same parallels and having equal bases are equal. The formula for the area of a parallelogram is proved in the next theorem. |
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