Prove that the diagonals of a parallelogram bisect each other.

Open in App

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.

Suggest Corrections

Similar questions

Prove logically the diagonals of a parallelogram bisect each other. Show conversely that a quadrilateral in which diagonals bisect each other is a parallelogram.

Q. If the diagonals of a quadrilateral bisect each other, then prove that it is a parallelogram.

Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.

Prove that if a diagonal of a quadrilateral bisect each other, it is a parallelogram.

Q. Diagonals of a parallelogram bisect each other.

Join BYJU'S Learning Program

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.