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**Property:** The diagonals of a parallelogram bisect each other .

**Given :** ABCD is parallelogram , AC & BD intersect at O.**To prove :** OA = OC and OB = OD .**Proof :** In ∆ AOB and ∆ COD , we know that

∠OAB = ∠ OCD (Alternate angle )

∠OBA = ∠ ODC (Alternate angle )

`bar (AB) = bar (CD)` (opposite sides are equal in parallelogram)

∆ AOB ≅ ∆ COD (ASA Axiom)

Hence OA = OC and OB = OD

#### Shaalaa.com | Property: The diagonals of a parallelogram bisect each other .

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