The diagonals of a parallelogram `A B C D` intersect at `OdotA` line through `O` intersects `A B` at `X` and `D C` at `Ydot` Prove that `O X=O Ydot`

Explanation

`ABCD` is a parallelogram.
`:. AB` parallel `DC`
Also `AC` is a transversal of `AB` parallel `DC`.
`:./_1=/_2` [Alternate interior angles]
Now in `/_\AXO` and `/_\CYO`, we have
`⇒∠1=∠2` [Alternate interior angles]
`=>/_3=/_4` [Vertically opposite angles]
`=>CO=OA` [Diagonals bisect each other]
`:./_\AXO~=/_\CYO` [`ASA` Criteria]
`:.OX=OY [CPCT]`
Hence Proved.