Question

In a figure AY is perpendicular to ZY and BY is perpendicualar to XY such that AY=ZY and BY=XY prove that AB=ZX

Answer 1

a/c to question,
AY is perpendicular to ZY and BY is perpendicular to XY.
so, it is clear that $\angle{ZYA}=\angle{XYB}=90^{\circ}$

$\implies\angle{ZYA}+\angle{AYX}=\angle{XYB}+\angle{AYX}$

$\implies\angle{ZYX}=\angle{AYB}$.....(1)

from ∆AYB and ∆XYZ,
AY = ZY [ a/c to question,it is given ]
BY = XY [ it is given ]
$\angle{AYB}=\angle{ZYX}$[ from equation (1) ]
from S - A - S congruence rule,
$\triangle{AYB}\cong\triangle{ZYX}$

we know, corresponding parts of congruent triangles are congruent.
so, AB = ZX [ hence proved ]

Answer 2

your answer is in the attached image

• hope it helps