Question

Part 3: Choose a proof method.

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


Given: WZX YZX;

Prove: ZX is a perpendicular bisector of WY

Answer 1

The given congruences are corresponding sides and angles of ΔWZX and ΔYZX. Segment ZX is congruent to itself, so ΔWZX ≅ ΔYZX by SAS.

Then ∠WXZ ≅ ∠YXZ and WX ≅ YX by CPCTC. The latter means X is a midpoint and that ZX is a bisector of WY. The former means the angles of the linear pair ∠WXZ and ∠YXZ must both be 90°, as they are both congruent and supplementary.

Therefore, ZX is perpendicular to WY and also its bisector.