Question

ABCD is a rectangle.X and Y are points on sides AD BC respectively such that AY=BX.prove that BY=AX and BAY=ABX

Answer 1

you can refer to the above pic
join AY and BX
in Tri. aby and Tri.bax
ab= ab (common)
ay=BX. (given)
angle aby= angle Bax. (all angles are perpendicular in a rectangle)
therefore
Tri. aby is congruent to Tri. Bax ( by sas rule)
there ax = by. ( by cpct)

Answer 2

proved that BY=AX and ∠BAY=∠ABX if ABCD is a rectangle.X and Y are points on sides AD BC respectively such that AY=BX

Step-by-step explanation:

ABCD is a rectangle.X and Y are points on sides AD BC respectively such that AY=BX

Now comparing Δ ABX  & ΔBAY

AB = BA   ( common)

BX  = AY  ( given)

∠BAX = ∠ABY = 90°  ( all angles of rectangle are 90°)

=> Δ ABX  ≅ ΔBAY

=> AX = BY

  ∠ABX = ∠BAY

Hence proved that BY=AX and ∠BAY=∠ABX

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