Problem preview

G-CO.9 Warmup M2-036-A13-V02

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

Lines \(\ell~\) and \(m\) are parallel, and \(\angle~1\) and \(\angle~2\) occupy corresponding positions along a transversal. Name the theorem that justifies their congruence and state the angle relationship.

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By the converse of the corresponding angles theorem, angle 1 equals angle 2.

Since angles 1 and 2 are corresponding angles, they are vertical angles, so angle 1 equals angle 2.

By the corresponding angles theorem, angle 1 equals angle 2.

By the alternate interior angles theorem, angle 1 equals angle 2.

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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