Question

ABCD is a square. X andY are points on side AD and BC respectively such that AY=BX.

Answer 1

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 triangles XAB and YBA
We have,
∠XAB = ∠YBA = 90o [From (i)]
BX = AY (Given)
AB = BA (Common side)
So, by RHS congruence rule, we have
Triangles XAB Congruent to Triangles YBA
BY=AX (By c.p.c.t)
Angle BAY =Angle ABX
Hence proved