Lesson 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

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?

Here are three polygons.

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 \(\frac 1 4\).

Which of these sets of angle measures could be the three angles in a triangle?

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

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

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

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

In the picture lines \(AB\) and \(CD\) are parallel. Find the measures of the following angles. Explain your reasoning.

1. \(\angle BCD\)
2. \(\angle ECF\)
3. \(\angle DCF\)