Unit 1, Lesson 2
Corresponding Parts and Scale Factors
Grade 7
2.3
Activity
Here is Triangle O, followed by a number of other triangles.
Right triangle O, has sides 3, 4, 5. Right triangle A has sides 2, 3 halves, 5 halves. B has sides 6.08 and 6.32. C has sides 6, 7, 8. Right triangle D has sides 2, 5, and 5.39. Right triangle E has sides 2, 2, and 2.38. Right triangle F has sides 6, 8, and 10. Right triangle G has sides 3, 4, and 5. Right triangle H has sides 2, 8 thirds, and 10 thirds.
Your teacher will assign you two of the triangles to look at.
- For each of your assigned triangles, is it a scaled copy of Triangle O? Be prepared to explain your reasoning.
- As a group, identify all the scaled copies of Triangle O in the collection. Discuss your thinking. If you disagree, work to reach an agreement.
- List all the triangles that are scaled copies in the table. Record the side lengths that correspond to the side lengths of Triangle O listed in each column.
Triangle O 3 4 5 - Explain or show how each copy has been scaled from the original (Triangle O).
Student Lesson Summary
A figure and its scaled copy have corresponding parts, or parts that are in the same position in relation to the rest of each figure. These parts could be points, segments, or angles. For example, Polygon 2 is a scaled copy of Polygon 1.
A polygon and its scaled copy. Polygon 1 is six sided with vertices labeled ABCDEF. Starting at top left corner is vertice A. Side AB slants down and to right with length 3. Side BC is horizontal with length 3 point 2. Side CD slants up and to right with length 2. Side DE slants down and to left with length 1 point 3. Side EF is horizontal with length 2. Side FA slants up and to left with length 2.8. Polygon 2 is labeled GHIJKL. The side lengths of polygon 2 correspond to polygon 1 in this way: AB corresponds to GH, BC corresponds to HI, CD corresponds to IJ, DE corresponds to JK, EF corresponds to KL, and FA corresponds to LG. Side lengths of polygon 2 are: GH is 6, HI is 6 point 4, IJ is 4, JK is 2 point 6, KL is 4, LG is 5 point 6.
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Each point in Polygon 1 has a corresponding point in Polygon 2.
For example, point corresponds to point and point corresponds to point . -
Each segment in Polygon 1 has a corresponding segment in Polygon 2.
For example, segment corresponds to segment . -
Each angle in Polygon 1 also has a corresponding angle in Polygon 2.
For example, angle corresponds to angle .
The scale factor between Polygon 1 and Polygon 2 is 2, because all of the lengths in Polygon 2 are 2 times the corresponding lengths in Polygon 1. The angle measures in Polygon 2 are the same as the corresponding angle measures in Polygon 1. For example, the measure of angle is the same as the measure of angle .
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 .