Mathematics
ABCD is a rectangle. X and Y are points on sides AD and BC respectively such that AY = BX. Prove that BY = AX and ∠BAY = ∠ABX.
Triangles
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Answer
In △ABY and △ABX,
AB = AB (Common)
∠XAB = ∠YBA (Each angle in rectangle is equal to 90°)
AY = BX (Given)
∴ △ABY ≅ △ABX (By RHS axiom)
We know that corresponding parts of congruent triangles are equal.
∴ BY = AX and ∠BAY = ∠ABX.
Hence, proved that BY = AX and ∠BAY = ∠ABX.
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