Illustrative Mathematics Grade 7, Unit 1, Lesson 2: Corresponding Parts and Scale Factors

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Illustrative Math
Grade 7

Lesson 2: Corresponding Parts and Scale Factors

Let’s describe features of scaled copies.

Illustrative Math Unit 7.1, Lesson 2 (printable worksheets)

Lesson 2 Summary

The following diagram describes how to identify corresponding points, corresponding segments, and corresponding angles and what the scale factor has to do with a figure and its scaled copy.

Lesson 2.1 Number Talk: Multiplying by a Unit Fraction

Find each product mentally. 1/4 · 32
(7.2) · 1/9
1/4 · (5.6)

• See Video for Whole Lesson

Lesson 2.2 Corresponding Parts

One road sign for railroad crossings is a circle with a large X in the middle and two R’s—with one on each side. Here is a picture with some points labeled and two copies of the picture. Drag and turn the moveable angle tool to compare the angles in the copies with the angles in the original.
Open Applet

1. Complete this table to show corresponding parts in the three pictures.
2. Is either copy a scaled copy of the original road sign? Explain your reasoning.
3. Use the moveable angle tool to compare angle KLM with its corresponding angles in Copy 1 and Copy 2. What do you notice?
4. Use the moveable angle tool to compare angle NOP with its corresponding angles in Copy 1 and Copy 2. What do you notice?

Lesson 2.3 Scaled Triangles

Here is Triangle O, followed by a number of other triangles.
Your teacher will assign you two of the triangles to look at.

1. For each of your assigned triangles, is it a scaled copy of Triangle O? Be prepared to explain your reasoning.
2. 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.
3. 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.
4. Explain or show how each copy has been scaled from the original (Triangle O).

Are you ready for more?

Choose one of the triangles that is not a scaled copy of Triangle O. Describe how you could change at least one side to make a scaled copy, while leaving at least one side unchanged.

Lesson 2 Practice Problems

1. The second H-shaped polygon is a scaled copy of the first.
   a. Show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. Consider using colored pencils to highlight corresponding parts or labeling some of the vertices.
   b. What scale factor takes the original polygon to its smaller copy? Explain or show your reasoning.
   
2. Figure B is a scaled copy of Figure A. Select all of the statements that must be true:
   A. Figure B is larger than Figure A.
   B. Figure B has the same number of edges as Figure A.
   C. Figure B has the same perimeter as Figure A.
   D. Figure B has the same number of angles as Figure A.
   E. Figure B has angles with the same measures as Figure A.
   
3. Polygon B is a scaled copy of Polygon A.
   a. What is the scale factor from Polygon A to Polygon B? Explain your reasoning.
   b. Find the missing length of each side marked with ? in Polygon B.
   c. Determine the measure of each angle marked with ? in Polygon A.
   
4. Complete each equation with a number that makes it true.
   a. 8 &midoot; _____ = 40
   b. 8 + _____ = 40
   c. 21 ÷ _____ = 7
   d. 21 − _____ = 7
   e. 21 · _____ = 7
   

The Open Up Resources math curriculum is free to download from the Open Up Resources website and is also available from Illustrative Mathematics.

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