# Lesson 1

Projecting and 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

### Solution

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### 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?

### Solution

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### Problem 3

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 $$\frac 1 4$$.

### Solution

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### 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:

$$70^\circ$$, $$80^\circ$$, $$90^\circ$$

### Solution

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(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.

1. $$\angle BCD$$
2. $$\angle ECF$$
3. $$\angle DCF$$

### Solution

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(From Unit 1, Lesson 14.)