Unit 2, Lesson 2
Scale Factors and Making Scaled Copies
Accelerated 7
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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.
| Triangle O | 3 | 4 | 5 |
|---|---|---|---|
Diego and Jada want to scale this polygon so the side that corresponds to 15 units in the original is 5 units in the scaled copy.
Diego and Jada each use a different operation to find the new side lengths. Here are their finished drawings.
Diego's drawing has 6 side lengths of 26, 8, 5, 2, 11, and 20, but the sides do not connect to form a closed figure.
Jada's drawing is a rectangle of height 10 and length 12 with a rectangle of height 4, length 5 removed from the bottom right corner.
Did each method produce a scaled copy of the polygon? Explain your reasoning.
Pause here for a whole-class discussion.
Creating a scaled copy involves multiplying the lengths in the original figure by a scale factor.
For example, to make a scaled copy of triangle where the base is 8 units, we would use a scale factor of 4. This means multiplying all the side lengths by 4, so in triangle , each side is 4 times as long as the corresponding side in triangle .
To create a scaled copy of a figure, all the side lengths in the original figure are multiplied by the same number. This number is called the scale factor.
In this example, the scale factor is 1.5, because , , and .