Problem preview

G-CO.9 Warmup M2-036-A14-V04

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

Choose the correct theorem or converse for lines, angles, and perpendicular bisectors

Problem

A point lies on the perpendicular bisector of a segment. Name the theorem that applies and state the endpoint-distance relationship it guarantees.

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This is the corresponding angles theorem, because perpendicular lines create matching angle relationships.

This is the same-side interior angles theorem, because lines and angle relationships can justify segment facts.

This is the converse of the perpendicular bisector theorem, because equal distances and perpendicular bisectors describe the same idea.

This is the perpendicular bisector theorem, because a point on the perpendicular bisector of a segment is equidistant from the segment’s endpoints.

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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: Choose the correct theorem or converse for lines, angles, and perpendicular bisectors