Unit 1, Lesson 2
Corresponding Parts and Scale Factors
Grade 7
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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 |
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 |
|---|---|---|---|
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.
Each point in Polygon 1 has a corresponding point in Polygon 2.
For example, point
Each segment in Polygon 1 has a corresponding segment in Polygon 2.
For example, segment
Each angle in Polygon 1 also has a corresponding angle in Polygon 2.
For example, 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
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
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