Unit 1, Lesson 14
Alternate Interior Angles
Grade 8
Preparation
Lesson Narrative
The purpose of this lesson is for students to connect rigid transformations with the congruence of angles created by a set of parallel lines cut by a transversal. Students identify angle measures on an image and describe what they notice about the angle measures using precise language (MP6). Then students use rotations to explain why a pair of alternate interior angles are congruent (MP3). Students may connect these arguments to ones they made in a previous lesson when they justified that vertical angles are congruent. Finally, students use their arguments to generalize that for any pair of parallel lines cut by a transversal, the two pairs of alternate interior angles are congruent.
In the optional activity, students have additional opportunities to analyze their arguments. They compare angles formed by parallel lines cut by a transversal to angles formed by a pair of non-parallel lines cut by a third line.
- Calculate angle measures using alternate interior, vertical, and supplementary angles to solve problems.
- Justify (orally and in writing) that alternate interior angles made by a transversal connecting two parallel lines are congruent using properties of rigid motions.
Let’s explore why some angles are always equal.
Required Preparation
None
Alternate interior angles are created when 2 parallel lines are crossed by another line. This line is called a transversal. Alternate interior angles are inside the parallel lines and on opposite sides of the transversal.
This diagram shows 2 pairs of alternate interior angles:
- Angles and
- Angles and
There are two horizontal parallel lines, and a third diagonal line drawn from the bottom left to the upper right, intersecting both horizontal lines. The diagonal line is labeled transversal. There are four angles created by the diagonal line inside the parallel lines. The upper left angle is labeled a, upper right is b, lower left is c, and lower right is d.