Answer:
The proof is given below.
Step-by-step explanation:
Given:
∠WZX ≅ ∠YZX
ZW ≅ ZY
To Prove:
ZX is a perpendicular bisector of WY
Proof:
In Δ WZX and Δ YZX
Statement Reasons
ZW ≅ ZY ……….{Given}
∠WZX ≅ ∠YZX …………..{Given}
ZX ≅ ZX ……….{Reflexive Property}
ΔWZX ≅ ΔYZX ….{Side-Angle-Side test}
WX ≅ YX ....{corresponding sides of congruent triangle or cpct}
∠ZXW ≅ ∠ZXY ...{corresponding angles of congruent triangle or cpct}
But W-X-Y is a straight Line
[tex]\angle ZXW +\angle ZXY = 180[/tex] ...Linear pair postulate
[tex]2\times \angle ZXW =180[/tex]
[tex]\angle ZXW =\dfrac{180}{2}=90\°[/tex]
∴ WX ≅ YX {ZX bisects WY}
∠ZXW ≅ ∠ZXY = 90° {ZX Perpendicular WY
∴ ZX is a perpendicular bisector of WY
