Question

Use a paragraph, flow chart, or two-column proof to prove that ZX is the perpendicular bisector of side WY.

Answer 1

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

$\angle ZXW +\angle ZXY = 180$       ...Linear pair postulate

$2\times \angle ZXW =180$

$\angle ZXW =\dfrac{180}{2}=90\°$

∴      WX ≅ YX                     {ZX bisects WY}

   ∠ZXW ≅ ∠ZXY = 90°     {ZX Perpendicular WY

∴ ZX is a perpendicular bisector of WY