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.
Given that ABCD is a square, X and Y are points on the 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 = 90o
∠XAB = ∠YBA = 90o (i)
Now, consider
We have,
∠XAB = ∠YBA = 90o [From (i)]
BX = AY (Given)
AB = BA (Common side)
So, by RHS congruence rule, we have
(By c.p.c.t)