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| Theorem 1 |
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| The diagonals of a parallelogram bisect each other. |
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| ABCD is a parallelogram in which diagonals AC and BD |
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| intersect each other at O. |
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| The diagonals AC and BD bisect each other i.e, AO=OC and BO=DO. |
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| AB||CD (by definition of parallelogram) |
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| AC is a transversal. |
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| (alternate angles are equal in a parallelogram) |
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| Also AB=DC (opposite sides are equal in a parallelogram) |
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| Now in D AOB and D COD, |
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| AB=DC (opposite sides of parallelogram are equal) |
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 (proved by (i)) |
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 D AOB D COD (AAS congruency condition) |
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 AO=OC and OB=OD (corresponding parts of congruent triangles are congruent) |
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| i.e., the diagonals of a parallelogram bisect each other. |
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| We have proved one of the properties of a parallelogram by logical deductions. |
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