Problem preview

G-CO.9 Warmup M2-036-A13-V03

Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.

Complete a proof involving lines, angles, or perpendicular bisectors

Problem

Point \(P\) satisfies \(PA~=~PB\) for segment \(AB\). Name the converse theorem that converts these equal endpoint distances into a location statement for \(P\), and state that location.

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By the converse of the perpendicular bisector theorem, P lies on the perpendicular bisector of AB.

Since PA = PB, P is the midpoint of AB, so it lies on the perpendicular bisector of AB.

By the perpendicular bisector theorem, P lies on the perpendicular bisector of AB.

Since PA = PB, AB is the perpendicular bisector of PB.

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Curriculum context

Course: Math II
Standard: G-CO.9
Category: Geometry
Domain: Congruence
Objective: Prove theorems about lines and angles: vertical angles, parallel-line angle relationships, and perpendicular bisectors.
Problem type: Complete a proof involving lines, angles, or perpendicular bisectors