Lesson 9: Moves in Parallel
About this lesson
The previous lesson examines the impact of rotations on line segments and polygons. This lesson focuses on the effects of rigid transformations on lines. In particular, students see that parallel lines are taken to parallel lines and that a \(180^\mathrm o\) rotation about a point on the line takes the line to itself. In grade 7, students found that vertical angles have the same measure, and they justify that here using a \(180^\mathrm o\) rotation.
As they investigate how \(180^\mathrm o\) rotations influence parallel lines and intersecting lines, students are looking at specific examples but their conclusions hold for all pairs of parallel or intersecting lines. No special properties of the two intersecting lines are used so the \(180^\mathrm o\) rotation will show that vertical angles have the same measure for any pair of vertical angles.
Lesson overview
 9.1 Warmup: Line Moves (10 minutes)

9.2 Activity: Parallel Lines (15 minutes)
 Includes "Are you Ready for More?" extension problem
 9.3 Activity: Let’s Do Some 180’s (15 minutes)
 Lesson Synthesis
 9.4 Cooldown: Finding Missing Measurements (5 minutes)
Learning goals:
 Comprehend that a rotation by 180 degrees about a point of two intersecting lines moves each angle to the angle that is vertical to it.
 Describe (orally and in writing) observations of lines and parallel lines under rigid transformations, including lines that are taken to lines and parallel lines that are taken to parallel lines.
 Draw and label rigid transformations of a line and explain the relationship between a line and its image under the transformation.
 Generalize (orally) that “vertical angles” are congruent using informal arguments about 180 degree rotations of lines.
Learning goals (student facing):
 Let’s transform some lines.
Learning targets (student facing):
 I can describe the effects of a rigid transformation on a pair of parallel lines.
 If I have a pair of vertical angles and know the angle measure of one of them, I can find the angle measure of the other.
Required materials:
 geometry toolkits
Glossary:
 vertical angles  Vertical angles are opposite angles that share the same vertex. They are formed by a pair of intersecting lines. Their angle measures are equal. For example, angles \(AEC\) and \(DEB\) are vertical angles. If angle \(AEC\) measures \(120^\circ\), then angle \(DEB\) must also measure \(120^\circ\). Angles \(AED\) and \(BEC\) are another pair of vertical angles.
 Access the complete Grade 8 glossary.
Standards:
 This lesson builds on the standard: CCSS.7.G.B.5MS.7.G.5
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 20172019 by Open Up Resources. It is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0). OUR's 6–8 Math Curriculum is available at https://openupresources.org/mathcurriculum/.
Adaptations and updates to IM 6–8 Math are copyright 2019 by Illustrative Mathematics, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
Adaptations to add additional English language learner supports are copyright 2019 by Open Up Resources, and are licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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