#### Question

ABCD is a square, X and Yare points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.

#### Solution

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

We have

∠XAB=∠YBA=90° ...........[From (1)]

BX=AY [given]

And AB=BA [Common side]

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

Is there an error in this question or solution?

Solution Abcd is a Square, X and Yare Points on Sides Ad and Bc Respectively Such that Ay = Bx. Prove that by = Ax and ∠Bay = ∠4bx. Concept: Criteria for Congruence of Triangles.