`A B C D` is a parallelogram. `A B` is produced to `E` so that `B E=A B` . Prove that `E D` bisects `B Cdot`

Explanation

Consider `triangle OCD` and `triangle OBE`
From the figure,
`angle DOC` and `angle EOB` are vertically opposite angles` angle DOC = angle EOB`
We know that, `AB `|| `CD` and `BC` is a transversal
`angle OCD` and `angle OBE` are alternate angles
`angle OCD = angle OBE`
From the figure,` AB = CD` and `BE = AB `
So ,
` DC = BE ` ( By AAS rule)
`triangle OCD ≅ triangle OBE `
`OC = OB (c. p. c. t)`
Therefore, it is proved that ` ED` bisects `BC`.