Corresponding Parts and Scale Factors: IM 7.1.2
[url=https://im.kendallhunt.com/MS/teachers/2/1/2/preparation.html]“Corresponding Parts and Scale Factors”[/url] from IM Grade 7 by [url=https://www.geogebra.org/m/gus8ffvr]Open Up Resources[/url] and Illustrative Mathematics. Licensed under the [url=https://creativecommons.org/licenses/by/4.0/]Creative Commons Attribution 4.0 license[/url].
Table of Contents
- Lesson
- IM 7.1.2 Lesson: Corresponding Parts and Scale Factors
- Practice
- IM 7.1.2 Practice: Corresponding Parts and Scale Factors
IM 7.1.2 Lesson: Corresponding Parts and Scale Factors
Find each product mentally.
[math]\frac{1}{4}\cdot32[/math]
[math]7.2\cdot\frac{1}{9}[/math]
[math]\frac{1}{4}\cdot5.6[/math]
A road sign for railroad crossings is a circle with a large X in the middle and two R’s. Here is a picture with some points labeled and two copies of the picture. Use the angle tool to compare the angles in the copies and in the original.
Complete this table to show corresponding parts in the three pictures.
Is either copy a scaled copy of the original road sign? Explain your reasoning.[br]
Use the moveable angle tool to compare angle KLM with its corresponding angles in Copy 1 and Copy 2.
What do you notice?
Use the moveable angle tool to compare angle NOP with its corresponding angles in Copy 1 and Copy 2.
What do you notice?
Here is Triangle O, followed by a number of other triangles.
[br]Which of the triangles is a scaled copy of Triangle O?
Explain your reasoning for choosing each triangle.
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.
Explain or show how each scaled copy triangle has been scaled from the original (Triangle O).
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.
IM 7.1.2 Practice: Corresponding Parts and Scale Factors
The second H-shaped polygon is a scaled copy of the first. Show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. Consider labeling corresponding parts or some of the vertices.
What scale factor takes the original polygon to its smaller copy? Explain or show your reasoning.[br]
Figure B is a scaled copy of Figure A. Select [b]all [/b]of the statements that must be true:
Polygon B is a scaled copy of Polygon A.
What is the scale factor from Polygon A to Polygon B? Explain your reasoning.
Find the missing length of each side marked with ? in Polygon B.
Determine the measure of each angle marked with ? in Polygon A.
Complete each equation with a number that makes it true.
[math]8\cdot\text{______}=40[/math]
[math]8+\text{______}=40[/math]
[math]21\div\text{______}=7[/math]
[math]21-\text{______}=7[/math]
[math]21\cdot\text{______}=7[/math]