Question

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.

Answer 1

Square = ABCD (Given)

X is the point on sides AD (Given)

Y is the point on side BC (Given)

AY = BX (Given)

Construction - Join B and X, A and Y.

Since, ABCD is a square, therefore -

∠DAB = ∠CBA = 90°

∠XAB =∠YBA = 90°      .....(1)  

Now, Considering ΔXAB and ΔYBA

∠XAB =∠YBA = 90°

BX = AY ( Given)

AB = BA ( Common)

Thus, by RHS congruency ΔXAB ≅ ΔYBA

Since, the corresponding parts of congruent triangles are equal.

Therefore, BY = AX and ∠BAY = ∠ABX.

Hence proved