Lesson 8
Projecting and Scaling
Let’s explore scaling.
Problem 1
Rectangle \(A\) measures 12 cm by 3 cm. Rectangle \(B\) is a scaled copy of Rectangle \(A\). Select all of the measurement pairs that could be the dimensions of Rectangle \(B\).
6 cm by 1.5 cm
10 cm by 2 cm
13 cm by 4 cm
18 cm by 4.5 cm
80 cm by 20 cm
Problem 2
Rectangle \(A\) has length 12 and width 8. Rectangle \(B\) has length 15 and width 10. Rectangle \(C\) has length 30 and width 15.
- Is Rectangle \(A\) a scaled copy of Rectangle \(B\)? If so, what is the scale factor?
- Is Rectangle \(B\) a scaled copy of Rectangle \(A\)? If so, what is the scale factor?
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Explain how you know that Rectangle \(C\) is not a scaled copy of Rectangle \(B\).
- Is Rectangle \(A\) a scaled copy of Rectangle \(C\)? If so, what is the scale factor?
Problem 3
Here are three polygons.
![Image of three polygons, A, B and C. A is a right triangle, B is a polygon and C is a parallelogram.](https://staging-cms-im.s3.amazonaws.com/qZVUxobx1ReD2ELGzK97ki18?response-content-disposition=inline%3B%20filename%3D%228-8.2.A1.newPP.Image.01.png%22%3B%20filename%2A%3DUTF-8%27%278-8.2.A1.newPP.Image.01.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T031707Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=2bd0324909659b230563d8086815d06cd5afa2317a4cc132151def117df0d8c6)
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Draw a scaled copy of Polygon A with scale factor \(\frac 1 2\).
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Draw a scaled copy of Polygon B with scale factor 2.
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Draw a scaled copy of Polygon C with scale factor \(\frac 1 4\).
Problem 4
In the picture lines \(AB\) and \(CD\) are parallel. Find the measures of the following angles. Explain your reasoning.
![Three lines in a plane.](https://staging-cms-im.s3.amazonaws.com/qHoeCXAiX9vsGTRWCN5wPeLE?response-content-disposition=inline%3B%20filename%3D%228-8.1.D.PP.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.1.D.PP.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240727%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240727T031707Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=27b9d21e636331ae1c58b1a2b329635e22e1b6e7a2be9539812c807162a9c24c)
- \(\angle BCD\)
- \(\angle ECF\)
- \(\angle DCF\)
Problem 5
Which of these sets of angle measures could be the three angles in a triangle?
\(40^\circ\), \(50^\circ\), \(60^\circ\)
\(50^\circ\), \(60^\circ\), \(70^\circ\)
\(60^\circ\), \(70^\circ\), \(80^\circ\)
\(70^\circ\), \(80^\circ\), \(90^\circ\)
Problem 6
Quadrilateral A has side lengths 3, 6, 6, and 9. Quadrilateral B is a scaled copy of A with a shortest side length equal to 2. Jada says, “Since the side lengths go down by 1 in this scaling, the perimeter goes down by 4 in total.” Do you agree with Jada? Explain your reasoning.