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| Theorem 3 |
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| The area of a triangle is half that of a parallelogram standing on the same base and between the same parallels. |
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 and a parallelogram ABCD are standing on the same base AB and between the same parallels AB, DC. |
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| Complete the parallelogram ABPQ. |
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| The area of a triangle is half that of a parallelogram standing on equal bases and between the same parallels. |
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| Triangles on the same base and between the same parallels are equal. |
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 and  are on the same base and between the same parallels AB, DQ. |
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| Complete the parallelograms ABCD and ABPQ. |
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| Triangles with equal areas on the same base have equal corresponding altitudes. |
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 and  are equal in area and are on the same base AB. PM and QN are altitudes. |
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| PM = QN |
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| Join PQ. |
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