Lesson 2Corresponding Parts and Scale Factors

Learning Goal

Let’s describe features of scaled copies.

Learning Targets

  • I can describe what the scale factor has to do with a figure and its scaled copy.

  • In a pair of figures, I can identify corresponding points, corresponding segments, and corresponding angles.

Lesson Terms

  • corresponding
  • scale factor
  • scaled copy

Warm Up: Number Talk: Multiplying by a Unit Fraction

Problem 1

Find each product mentally.

Activity 1: Corresponding Parts

Problem 1

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 in presentation mode

  1. Complete this table to show corresponding parts in the three figures.

    original

    copy 1

    copy 2

    point

    segment

    segment

    point

    angle

    angle

  2. Is either copy a scaled copy of the original figure? Explain your reasoning.

  3. Use the moveable angle tool to compare angle with its corresponding angles in Copy 1 and Copy 2. What do you notice?

  4. Use the moveable angle tool to compare angle with its corresponding angles in Copy 1 and Copy 2. What do you notice?

Print Version

Here is a figure and two copies, each with some points labeled.

Original sign is 18 inches tall and 18 inches wide. Copy 1 is 14 inches tall and 14 inches wide. Copy 2 is 17 inches tall and 26 inches wide.

  1. Complete this table to show corresponding parts in the three figures.

    original

    copy 1

    copy 2

    point

    segment

    segment

    point

    angle

    angle

  2. Is either copy a scaled copy of the original figure? Explain your reasoning.

  3. Use tracing paper to compare angle with its corresponding angles in Copy 1 and Copy 2. What do you notice?

  4. Use tracing paper to compare angle with its corresponding angles in Copy 1 and Copy 2. What do you notice?

Activity 2: Scaled Triangles

Problem 1

Here is Triangle , 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.

  1. For each of your assigned triangles, is it a scaled copy of Triangle ? Be prepared to explain your reasoning.

  2. As a group, identify all the scaled copies of Triangle 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 listed in each column.

    Triangle

    3

    4

    5

  4. Explain or show how each copy has been scaled from the original (Triangle ).

Are you ready for more?

Problem 1

Choose one of the triangles that is not a scaled copy of Triangle .

Describe how you could change at least one side to make a scaled copy, while leaving at least one side unchanged.

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.

Polygon 1 is A, F, E, D, C, B with side lengths, 2.8, 2, 1.3, 2, 3.2, and 3. Polygon 2 is G, L, K, J, I, H with side lengths 5.6, 4, 2.6, 4, 6.4, and 6.

  • 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 .