# Angle Relationships

Videos, examples, and solutions to help Grade 8 students learn how to use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles.

For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.

Common Core: 8.G.5

### Suggested Learning Targets

• I can define similar triangles.
• I can define and identify transversals.
• I can identify angles created when a parallel line is cut by transversal (alternate
interior, alternate exterior, corresponding, vertical, adjacent, etc.).
• I can justify that the sum of the interior angles equals 180. (For example, arrange
three copies of the same triangle so that the three angles appear to form a line).
• I can justify that the exterior angles of a triangle is equal to the sum of the two
remote interior angles.
• I can use Angle-Angle Criterion to prove similarity among triangles. (Give an
argument in terms of transversals why this is so).

Understanding angle sum, exterior angles, and other properties (8.G.5)

Angle Relationships 1 (8.G.5)
Supplementary angles are adjacent angles that form a line. Their measures add to 180°
Vertical angles are the opposite angles when 2 lines form. Vertical angles have equal measures.
Corresponding angles and alternate interior angles have equal measures.

8.G.5 - Angle Relationships

Transversals and Right Angles 8.G.5

Angle Relationships with Parallel Lines - Part 1
This video discusses the three angle relationships, with regards to parallel lines, that are congruent to each other. These angle relationships are alternate interior angles, alternate exterior angles, and corresponding angles. I also go into detail explaining the basics behind transversals and parallel lines.

Angle Relationships with Parallel Lines - Part 2
This video discusses the two angle relationships, with regards to parallel lines, that are supplementary angles to each other. These angle relationships are consecutive interior angles, otherwise known as same-side interior angles, and consecutive exterior angles, otherwise known as same-side exterior angles.

Angle Relationships with Parallel Lines - Part 3
This video explains how to solve the harder types of problems when it comes to angle relationships and parallel lines.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations. 