The diogonals AC and BD of a parallelogram ABCD bisect each other at O A line segment XY through - Maths - Understanding Quadrilaterals

Question

The diogonals AC and BD of a parallelogram ABCD bisect each
other at O A line segment XY through O has its end-points on the
pposite sides AB and CD Is XY also bisected at O

Lalit Mehra · Accepted Answer

Given : ABCD is a parallelogram Diagonals AB and BD intersect at O XY passes through O and intersects AB and CD in X and Y respectively To Prove : OX = OY Proof : We know that, the diagonals of the parallelogram bisect each other âˆ´ OA = OC In Î”AOX and Î”COY, âˆ OAX = âˆ OCY (Pair of alternate angles) OA = OC âˆ AOX= âˆ COY (Vertically opposite angles) âˆ´Î”AOX $≅$ Î”COY (ASA congruence Criterion) â‡’ OX = OY (CPCT) Thus, XY is bisected at O

The diogonals AC and BD of a parallelogram ABCD bisect each other at O. A line segment XY through O has its end-points on the pposite sides AB and CD. Is XY also bisected at O.