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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 -

Given : In square ABCD, X and Y are points on side AD and BC respectively and AY = BX
 
To prove : BY = AX
∠BAY = ∠ABX
Proof: In right ∆BAX and ∆ABY
AB =AB (Common)
Hyp. BX = AY (Given)
∴ ∆BAX ≅ ∆ABY (RHS axiom)
∴ AX = BY (c.p.c.t.)
∠ABX = ∠BAY (c.p.c.t.)
Hence, BY = AX and ∠BAY = ∠ABX.

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