Question

Prove that the diagonals of a parallelogram bisect each other and given conditions are
ABCD is a parallelogram, in which AB II DC
and AD II BC, and the diagonals AC and BD intersect at the point O.


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Answer 1

Answer:

Given : ||gm ABCD in which diagonals AC and BD bisect each other.

To Prove : OA = OC and OB = OD

Proof : AB || CD (Given)

∠1 = ∠2 (alternate ∠s)

∠3 = ∠4 = (alternate ∠s)

and AB = CD (opposite sides of //gm)

∆COD = ∆AOB (A.S.A. rule)

OA = OC and OB = OD

Hence the result.