In previous lessons, students looked at the relationship between a figure and a scaled copy by finding the scale factor that relates the side lengths and by using tracing paper to compare the angles. This lesson takes both of these comparisons a step further.
- Students study corresponding distances between points that are not connected by segments, in both scaled and unscaled copies. They notice that when a figure is a scaled copy of another, corresponding distances that are not connected by a segment are also related by the same scale factor as corresponding sides.
- Students use protractors to test their observations about corresponding angles. They verify in several sets of examples that corresponding angles in a figure and its scaled copies are the same size.
Students use both insights—about angles and distances between points—to make a case for whether a figure is or is not a scaled copy of another (MP3). Practice with the use of protractors will help develop a sense for measurement accuracy, and how to draw conclusions from said measurements, when determining whether or not two angles are the same.
Lesson overview
- 4.1 Warm-up: Three Quadrilaterals (Part 1) (5 minutes)
- 4.2 Activity: Three Quadrilaterals (Part 2) (10 minutes)
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4.3 Activity: Scaled or Not Scaled? (10 minutes)
- Includes "Are you Ready for More?" extension problem
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4.4 Optional Activity: Comparing Pictures of Birds (10 minutes)
- There is a digital applet in this activity.
- Lesson Synthesis
- 4.5 Cool-down: Corresponding Polygons (5 minutes)
Learning goals:
- Explain (orally and in writing) that corresponding angles in a figure and its scaled copies have the same measure.
- Identify (orally and in writing) corresponding distances or angles that can show that a figure is not a scaled copy of another.
- Recognize that corresponding distances in a figure and its scaled copy are related by the same scale factor as corresponding sides.
Learning goals (student facing):
- Let’s find relationships between scaled copies.
Learning targets (student facing):
- I can use corresponding distances and corresponding angles to tell whether one figure is a scaled copy of another.
- When I see a figure and its scaled copy, I can explain what is true about corresponding angles.
- When I see a figure and its scaled copy, I can explain what is true about corresponding distances.
Required materials:
- geometry toolkits
Required preparation:
- Make sure students have access to their geometry toolkits, especially rulers and protractors.
Glossary:
- Access the complete Grade 7 glossary.
IM 6–8 Math was originally developed by Open Up Resources and authored by Illustrative Mathematics, and is copyright 2017-2019 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/math-curriculum/.
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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