Videos and solutions to help Grade 8 students learn about the relationships between angles associated with parallel lines.

New York State Common Core Math Grade 8, Module 2, Lesson 12.

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Common Core For Grade 8

Student Outcomes

Students know that corresponding angles, alternate interior angles, and alternate exterior angles of parallel lines are equal. Students know that when these pairs of angles are equal, then lines are parallel.

Students know that corresponding angles of parallel lines are equal because of properties related to translation. Students know that alternate interior angles of parallel lines are equal because of properties related to rotation.

Students present informal arguments to draw conclusions about angles formed when parallel lines are cut by a transversal.

**Corresponding angles**: angles that are on the same side of the transversal in corresponding positions.

** Alternate interior angles**: angles that are on opposite sides of the transversal
and between (or inside) the 2 parallel lines.

** Alternate exterior angles**: angles that are
on opposite sides of the transversal
and outside the two parallel lines.

Exploratory Challenge 1

In the figure below, L_{1} is not parallel to L_{2}, and m is a transversal. Use a protractor to measure angles 1–8. Which, if any, are equal? Explain why. (Use your transparency, if needed).

Exploratory Challenge 2

In the figure below, L_{1} || L_{2} and m is a transversal. Use a protractor to measure angles 1–8. List the angles that are equal in measure.

a. What did you notice about the measures of ∠1 and ∠5? Why do you think this is so? (Use your transparency, if needed).

b. What did you notice about the measures of ∠3 and ∠7? Why do you think this is so? (Use your transparency, if needed.) Are there any other pairs of angles with this same relationship? If so, list them.

c. What did you notice about the measures of ∠4 and ∠6? Why do you think this is so? (Use your transparency, if needed). Is there another pair of angles with this same relationship?

**Theorem**: When parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent, the pairs of alternate interior angles are congruent, and the pairs of alternate exterior angles are congruent.

The **converse** of the theorem states that if you know that corresponding angles are congruent, then you can be sure that the lines cut by a transversal are parallel.

- When alternate interior angles are congruent, then the lines cut by a transversal are parallel.
- When alternate exterior angles are congruent, then the lines cut by a transversal are parallel.