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| Converse of Theorem 6 |
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| If in a parallelogram, the diagonals are equal and perpendicular, then it is a square. |
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| ABCD is a parallelogram. |
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| AC=BD and AC ^ BD |
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| ABCD is a square. |
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| Since the diagonals AC and BD are equal, |
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| ABCD is a rectangle - - -(i) |
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| (Diagonal property of rectangle) |
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| Since the diagonals are perpendicular to each other. |
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| ABCD is a rhombus. |
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 AB=AD - - -(ii) |
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| ABCD is a rectangle. (from i) |
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| With consecutive sides equal. (from ii) |
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 ABCD is a square. (by definition of a square) |
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| Hence the theorem is proved. |
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