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| Converse of Theorem 4 |
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| Now consider the converse of this theorem. |
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| If two diagonals of a parallelogram are equal, it is a rectangle. |
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| ABCD is a parallelogram in which AC=BD. |
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| Parallelogram ABCD is a rectangle. |
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| In triangles ABC and DBC, |
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| AB=DC (opposite sides of parallelogram) |
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| BC=BC (common side) |
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| AC=BD (given) |
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 (corresponding parts of |
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| corresponding triangles) |
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| But these angles are consecutive interior angles on the same side of transversal BC and AB||DC. |
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 By definition of rectangle, parallelogram ABCD is a rectangle. |
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| Hence the theorem is proved. |
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