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Question
If X and Y are points on sides AD and BC respectively of square ABCD such that AY = BX, then BY is always equal to
If X and Y are points on sides AD and BC respectively of square ABCD such that AY = BX, then BY is always equal to
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Solution
The correct option is D AX
Given that ABCD is square.
∴ ∠A = ∠B = ∠C = ∠D = 90°
Now, in ΔXAB and ΔYBA,
∠XAB = ∠YBA (Each 90°)
XB = YA (Given)
AB = BA (Common)
∴ ΔXAB ≅ ΔYBA (RHS congruence rule)
⇒ BY = AX (CPCT)
Thus, BY is always equal to AX.
Hence, the correct answer is option (d).
Given that ABCD is square.
∴ ∠A = ∠B = ∠C = ∠D = 90°
Now, in ΔXAB and ΔYBA,
∠XAB = ∠YBA (Each 90°)
XB = YA (Given)
AB = BA (Common)
∴ ΔXAB ≅ ΔYBA (RHS congruence rule)
⇒ BY = AX (CPCT)
Thus, BY is always equal to AX.
Hence, the correct answer is option (d).
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