Two lines `A B` and `C D` intersect at `O` such that `B C` is equal and parallel to `A Ddot` Prove that the lines `A B` and `C D` bisect at `Odot`

Explanation

Such that `BC ∥ AD`
and ` BC = AD …….(i) `
To prove :` AB `and `CD` bisect at `O`.
First we have to prove that `triangleAOD cong triangle BOC`
`angleOCB=angleODA` [AD||BC and CD is transversal]
`AD = BC` [from (i)]
`angleOBC = angleOAD` [AD||BC and AB is transversal
] By` ASA `Criterion: `triangleAOD cong triangle BOC`
` OA = OB `and `OD = OC` (By c.p.c.t.)
Therefore, `AB` and `CD` bisect each other at `O`.
Hence Proved.