Question

ABCD is a square X and Y are points on sides AD and BC respectively such that AY is equal to BX prove that B Y is equal to AX and Angle B A Y is equal to angle ABX

Answer 1

right angled triangles BAY and ABX, AY = BX [Given data] BA = BA [Common side] ΔBAY ≅ ΔBAX [RHS axiom]
BY = AX [Corresponding sides of congruent triangles]
Also

Answer 2

Given :-

» ABCD is a square in which X and Y are point on AD and BC

=> AY = BX

___________________

In ΔABX and ΔBAY

=> BX = AY____[GIVEN]

=> AB = AB _____[COMMON]

=> angle(XAB) = angle(YBA) = 90

therefore :-

=> ΔABX ≈ ΔBAY [by SOS congruent criterion]
______________[PROVED]

___________________

then

=> AX = BY [by corresponding parts of congruent triangle (cpct) ]
________________[PROVED]

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