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.
Complete this table to show corresponding parts in the three figures.
original
copy 1
copy 2
point
segment
segment
point
angle
angle
Is either copy a scaled copy of the original figure? Explain your reasoning.
Use the moveable angle tool to compare angle
with its corresponding angles in Copy 1 and Copy 2. What do you notice? 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.
Complete this table to show corresponding parts in the three figures.
original
copy 1
copy 2
point
segment
segment
point
angle
angle
Is either copy a scaled copy of the original figure? Explain your reasoning.
Use tracing paper to compare angle
with its corresponding angles in Copy 1 and Copy 2. What do you notice? 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
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
? Be prepared to explain your reasoning. As a group, identify all the scaled copies of Triangle
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
listed in each column. Triangle
3
4
5
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.
Each point in Polygon 1 has a corresponding point in Polygon 2.
For example, pointcorresponds to point and point corresponds to point . Each segment in Polygon 1 has a corresponding segment in Polygon 2.
For example, segmentcorresponds to segment . Each angle in Polygon 1 also has a corresponding angle in Polygon 2.
For example, anglecorresponds 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