Question

prove that the 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:

ABCD is a parallelogram, diagonals AC and BD intersect at O

In triangles AOD and COB,

DAO = BCO (alternate interior angles)

AD = CB

ADO = CBO (alternate interior angles)

AOD COB (ASA)

Hence, AO = CO and OD = OB (c.p.c.t)

Thus, the diagonals of a parallelogram bisect each other.