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:
- Identify corresponding lengths and angles that can show that a figure is not a scaled copy of another.
- Understand and explain how corresponding distances between points and corresponding angles behave in a figure and its scaled copies.
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.
Adapted from Open Up Resources under CC BY license. All adaptations copyright LearnZillion.