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Kinds of Quadrilaterals - Diagonals of a Parallelogram

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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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