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| Converse of Theorem 5 |
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| If the diagonals of a parallelogram are perpendicular then it is a rhombus. |
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ABCD is a parallelogram in which AC and BD are perpendicular to each other.
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| ABCD is a rhombus. |
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| Let AC and BD intersect at right angles at O. |
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| In triangles AOD and COD, |
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| AO=OC (diagonals bisect each other) |
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| OD=OD (common side) |
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| AD = DC |
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| i.e., the adjacent sides are equal. |
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 By definition, ABCD is a rhombus. |
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| Hence the theorem is proved. |
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