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)



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