In Figure, `A B C D` is a parallelogram and `X and Y` are points on the diagonal `B D` such that `D X=B Y` . Prove that `A X C Y` is a parallelogram (ii) `A X=C Y , A Y=C X` ` A Y B cong C X D` (iv) ` A X Dcong C Y B`

Explanation

To prove the statements given in the question, we will follow these steps systematically.

### Given:
- \(ABCD\) is a parallelogram.
- Points \(X\) and \(Y\) are on diagonal \(BD\) such that \(DX = BY\).

### To Prove:
1. \(AXCY\) is a parallelogram.
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