Question

Prove that diagonals of a parallelogram bisect each other.

Answer 1

Consider a parallelogram with sides $ABCD$ in which diagonals $AC$ and $BD$ bisect each other.

We have to Prove that $OA=OC$ and $OB=OD$.

$AB\left|\right|CD$

$\angle DAC=\angle BCA$………(alternate angles)

$\angle ADB=\angle CBD$………(alternate angles)

$AB=CD$…………. (opposite sides of parallelogram)

$∆COD\cong ∆AOB$………… (A.S.A. rule)

$OA=OC$ and $OB=OD$

Therefore, diagonals of a parallelogram bisect each other.