Question

Prove that two diagonals of a parallelogram bisect each other.

Answer 1

Make diagonals
Take any two triangles opposite to each other formed by making diagonal
Prove them congruent
Alternate angles will be equal as opposite sides are equal
And one vertically opposite angle
Proof by AAA by CPCTC sides are also equal

Answer 2

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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)