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| Theorem 2 |
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| If the diagonals of a quadrilateral bisect each other then the quadrilateral is a parallelogram. |
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| ABCD is a quadrilateral in which diagonals AC and BD |
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| intersect at O such that AO=OC and BO=OD. |
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| ABCD is a parallelogram. |
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| In triangles AOB and COD, |
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| AO = CO (given) |
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| BO = OD (given) |
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 (vertically opposite angles are equal) |
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 D AOB  D COD (SAS congruency condition) |
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| Since these are alternate angles made by the transversal AC intersecting AB and CD. |
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 AB||CD |
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| Similarly, AD||BC |
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| Hence ABCD is a parallelogram. |
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