Vocabulary

Parallel lines are two or more lines that never intersect.

Transversal line is a line that passes through two lines in the same plane at two distinct points.

Corresponding angles are in the same position relative to the transversal and each of the parallel lines.

Alternate interior angles are on opposite sides of the transversal and between the parallel lines. 

Alternate exterior angles are on opposite sides of the transversal and on the outside of the parallel lines.

Linear pair: Two adjacent angles whose noncommon sides form a line are a linear pair. The sum of the measures of the angles in a linear pair is 180 degrees.​

Vertical angles are two angles that are formed by intersecting lines. They are not adjacent but share a vertex. Vertical angles have the same measure.​

Concept

Identify vertical, alternate interior, alternate exterior, corresponding, or linear pairs provided a pair of parallel lines and one transversal.

Rules

Corresponding angles are in the same position relative to the transversal and each of the parallel lines. For example, angles 1 and 5 or 3 and 7.​

Alternate interior angles are on opposite sides of the transversal and between the parallel lines. For example, angles 4 and 6.​

Alternate exterior angles are on opposite sides of the transversal and on the outside of the parallel lines. For example, angles 2 and 8.​

Linear pair: Two adjacent angles whose noncommon sides form a line are a linear pair. The sum of the measures of the angles in a linear pair is 180 degrees.​

Vertical angles are two angles that are formed by intersecting lines. They are not adjacent but share a vertex. Vertical angles have the same measure.​

Example

Which pair of angles represent vertical angles? 

Solution

Vertical angles are angles that share the same vertex but do not share a side. 

Only angle 1 and angle 3 fit that description. 

Pre-requisite Skills

Lines (8.6.1)

Complementary and Supplementary Angles (7.8.3)

Angle Relationships (6.10.5)