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ABCD is a square, X and Y are points on sides AD and BC respectively such that AY=BX. Prove that BY=AX and `/_BAY=/_ABX`.

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Given:`AY=BX`
`ABCD` is a square
To prove: `/_BAY=/_ABX`
Proof: In `/_\ABY` and `/_\ABX`
`AB=AB` (common)
`AY=BX` (given)
`/_XAB=/_YBA` (`90^@` each)
`:./_\ABY~=/_\ABX`
`:.` By `C.P.C.T /_BAY=/_ABX`
Hence Proved.
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