# Lesson 4

Scaled Relationships

Let’s find relationships between scaled copies.

### Problem 1

Select all the statements that must be true for any scaled copy Q of Polygon P.

A:

The side lengths are all whole numbers.

B:

The angle measures are all whole numbers.

C:

Q has exactly 1 right angle.

D:

If the scale factor between P and Q is $$\frac15$$, then each side length of P is multiplied by $$\frac15$$ to get the corresponding side length of Q.

E:

If the scale factor is 2, each angle in P is multiplied by 2 to get the corresponding angle in Q.

F:

Q has 2 acute angles and 3 obtuse angles.

### Problem 2

Here is Quadrilateral $$ABCD$$.

Quadrilateral $$PQRS$$ is a scaled copy of Quadrilateral $$ABCD$$. Point $$P$$ corresponds to $$A$$, $$Q$$ to $$B$$, $$R$$ to $$C$$, and $$S$$ to $$D$$.

If the distance from $$P$$ to $$R$$ is 3 units, what is the distance from $$Q$$ to $$S$$? Explain your reasoning.

### Problem 3

Figure 2 is a scaled copy of Figure 1.

1. Identify the points in Figure 2 that correspond to the points $$A$$ and $$C$$ in Figure 1. Label them $$P$$ and $$R$$. What is the distance between $$P$$ and $$R$$?
2. Identify the points in Figure 1 that correspond to the points $$Q$$ and $$S$$ in Figure 2. Label them $$B$$ and $$D$$. What is the distance between $$B$$ and $$D$$?
3. What is the scale factor that takes Figure 1 to Figure 2?
4. $$G$$ and $$H$$ are two points on Figure 1, but they are not shown. The distance between $$G$$ and $$H$$ is 1. What is the distance between the corresponding points on Figure 2?

### Problem 4

To make 1 batch of lavender paint, the ratio of cups of pink paint to cups of blue paint is 6 to 5. Find two more ratios of cups of pink paint to cups of blue paint that are equivalent to this ratio.