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?

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.

Draw a scaled copy of Polygon A with scale factor \(\frac 1 2\).

Draw a scaled copy of Polygon B with scale factor 2.

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.
 \(\angle BCD\)
 \(\angle ECF\)
 \(\angle DCF\)
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.