Question

prove that diagonal of parallelogram bisect each other ​

Answer 1

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Let consider a parallelogram ABCD in which AB||CD and AD||BC.

In ∆AOB and ∆COD , we have

∠DCO=∠OAB (ALTERNATE ANGLE)

∠CDO= ∠OBA. (ALTERNATE ANGLE)

AB=CD. (OPPOSITE SIDES OF ||gram)

therefore , ∆ AOB ≅ ∆COD. (ASA congruency)

hence , AO=OC and BO= OD. (C.P.C.T)

Answer 2

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 diagonal of parallelogram bisect each other .