Given that ABCD is a square, X and Y are points on sides AD and BC respectively such that AY =BX
We have to prove BY = AX and ∠BAY = ∠ABX.
Join B and X, A and Y.
Since, ABCD is a square
∠DAB = ∠CBA = 90°
∠XAB =∠YBA = 90° .....(1)
Now, consider triangle XAB and YBA
So, by RHS congruence criterion,
we have ΔXAB≅ΔYBA
Now, we know that corresponding parts of congruent triangles are equal.
∴ BY = AX and ∠BAY = ∠ABX.
∴ Hence proved