Lesson 7: No Bending or Stretching
About this lesson
In this lesson, students begin to see that translations, rotations, and reflections preserve lengths and angle measures, and for the first time call them rigid transformations. In earlier lessons, students talked about corresponding points under a transformation. Now they will talk about corresponding sides and corresponding angles of a polygon and its image.
As students experiment with measuring corresponding sides and angles in a polygon and its image, they will need to use the structure of the grid (MP7) as well as appropriate technology, including protractors, rulers, and tracing paper.
Lesson overview
 7.1 Warmup: Measuring Segments (5 minutes)

7.2 Activity: Sides and Angles (15 minutes)
 There is a digital applet in this activity.

7.3 Activity: Which One? (10 minutes)
 Includes "Are you Ready for More?" extension problem
 There is a digital applet in this activity.
 Lesson Synthesis
 7.4 Cooldown: Translated Trapezoid (5 minutes)
Learning goals:
 Comprehend that the phrase “rigid transformation” refers to a transformation where all pairs of “corresponding distances” and “corresponding angle” measures in the figure and its image are the same.
 Draw and label a diagram of the image of a polygon under a rigid transformation, including calculating side lengths and angle measures.
 Identify (orally and in writing) a sequence of rigid transformations using a drawing of a figure and its image.
Learning goals (student facing):
 Let’s compare measurements before and after translations, rotations, and reflections.
Learning targets (student facing):
 I can describe the effects of a rigid transformation on the lengths and angles in a polygon.
Required materials:
 geometry toolkits
Glossary:
 corresponding  When part of an original figure matches up with part of a copy, we call them corresponding parts. These could be points, segments, angles, or distances. For example, point \(B\) in the first triangle corresponds to point \(E\) in the second triangle. Segment \(AC\) corresponds to segment \(DF\).
 rigid transformation  A rigid transformation is a move that does not change any measurements of a figure. Translations, rotations, and reflections are rigid transformations, as is any sequence of these.
 Access the complete Grade 8 glossary.
Standards:
 This lesson builds on the standard:CCSS.4.MD.A
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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