Question

ABCD is a square, X and Y are points on sides AD and BC respectively such tht AY = BX, Prove that BY = AX and $\angle BAY=\angle ABX.$

Answer 1

Given : In square ABCD, X and Y are points on side AD and BC respectively and AY = BX

To prove : BY = AX

$\angle BAY=\angle ABX$

Proof : In right $\Delta BAXand\Delta ABY$

AB = AB (Common)

Hyp. BX = AY (Given)

$\therefore \Delta BAX\cong \Delta ABY\text{(RHS axiom)}$

$\therefore AXY=BY(c.p.c.t.)$

$\angle ABX=\angle BAY(c.p.c.t.)$

Hence, $BY=AXand\angle BAY=\angle ABX$