Question

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

Answer 1

The proof is given below.

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* \angle ZXW =180`

`\angle ZXW =(180)/(2)=90\°`

∴ WX ≅ YX {ZX bisects WY}

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

∴ ZX is a perpendicular bisector of WY