Prove that the diagonals of a parallelogram bisect each other.

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Solution

Parallelogram 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 parallelogram)
$△ C O D = △ A O B (A.S.A rule)$
$O A = O C and O B = O D$
Hence the result.

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Prove that the diagonals of a parallelogram bisect each other.

Parallelogram 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 parallelogram) △COD=△AOB(A.S.A rule) OA=OC and OB=OD Hence the result.