Lesson 1
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=fc050484953fefef4af139f0601ede1a4b7e1a7b614a2bc8c0ecd4203f34f0ec)
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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
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 5
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%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T143520Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=994ad8b555e45d7bb16d227cb5e0fcb952befea863f3211e5fcc0fcea5d865eb)
- \(\angle BCD\)
- \(\angle ECF\)
- \(\angle DCF\)