Unit 1, Lesson 2
Corresponding Parts and Scale Factors
Grade 7
Preparation
Lesson Narrative
This lesson develops the vocabulary for talking about scaling and scaled copies more precisely and for identifying the structures in common between two figures. Specifically, students learn to use the term corresponding to refer to a pair of points, segments, or angles in two figures that are scaled copies. Students also begin to describe the numerical relationship between the corresponding lengths in two figures using a scale factor. They see that when two figures are scaled copies of one another, the same scale factor relates their corresponding lengths. As students identify corresponding parts, they are making use of structure (MP7). As students identify the scale factor that relates corresponding sides, they are making use of repeated reasoning (MP8).
A look at the angles of scaled copies also begins in this lesson. Students use tracing paper to trace and compare angles in an original figure and its copies. They observe that in scaled copies the measures of corresponding angles are equal.
- Comprehend the phrase “scale factor” and explain (orally) how it relates corresponding lengths of a figure and its scaled copy.
- Explain (orally) what it means to say one part in a figure “corresponds” to a part in another figure.
- Identify and describe (orally and in writing) corresponding points, corresponding segments, or corresponding angles in a pair of figures.
Let’s describe features of scaled copies.
Required Materials
Activity 2
Required Preparation
Prepare to display the images of the railroad crossing sign.
For the digital version of the activity, acquire devices that can run the applet.
Corresponding parts are the parts that match up between a figure and its scaled copy. They have the same relative position. Points, segments, angles, or distances can be corresponding.
Point in the first triangle corresponds to point in the second triangle. Segment corresponds to segment .