# 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.

The side lengths are all whole numbers.

The angle measures are all whole numbers.

Q has exactly 1 right angle.

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.

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

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.

- 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 \(R\)?
- 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 \(D\)?
- What is the scale factor that takes Figure 1 to Figure 2?
- \(G\) 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.