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 \(B\).

A:

6 cm by 1.5 cm

B:

10 cm by 2 cm

C:

13 cm by 4 cm

D:

18 cm by 4.5 cm

E:

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.

  1. Is Rectangle \(A\) a scaled copy of Rectangle \(B\)? If so, what is the scale factor?
  2. Is Rectangle \(B\) a scaled copy of Rectangle \(A\)? If so, what is the scale factor?

  3. Explain how you know that Rectangle \(C\) is not a scaled copy of Rectangle \(B\).

  4. 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.

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

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

  3. 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?

A:

\(40^\circ\), \(50^\circ\), \(60^\circ\)

B:

\(50^\circ\), \(60^\circ\), \(70^\circ\)

C:

\(60^\circ\), \(70^\circ\), \(80^\circ\)

D:

\(70^\circ\), \(80^\circ\), \(90^\circ\)

(From Unit 1, Lesson 15.)

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. 
  1. \(\angle BCD\)
  2. \(\angle ECF\)
  3. \(\angle DCF\)
(From Unit 1, Lesson 14.)