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| Theorem 6 |
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| The diagonals of a square are equal and perpendicular to each other. |
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| ABCD is a square. |
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| AC and BD are diagonals intersecting at O. |
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| AB=AD (sides of a square are equal) |
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| AB||DC (opposite sides of a square are parallel) |
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 ABCD is parallelogram with consecutive sides equal. |
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 ABCD is a rhombus. (by definition) |
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| Since the diagonals of a rhombus are perpendicular to each other, AC ^ BD. |
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 ABCD is a parallelogram. |
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 ABCD is a rectangle with a pair of its consecutive sides equal. |
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| Since the diagonals of a rectangle are equal, AC=BD. |
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 Diagonal AC=Diagonal BD and AC ^ BD |
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| Hence the theorem is proved. |
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