# Lesson 12

Practice With Proportional Relationships

- Let’s find unknown values in proportional relationships.

### Problem 1

Quadrilateral \(ABCD\) is similar to quadrilateral \(A’B’C’D’\). Select **all** statements that must be true.

\(\frac{A’B’}{AB}=\frac{A’C’}{AC}\)

\(\frac{AD}{A’D’}=\frac{BC}{B’C’}\)

\(\frac{BD}{B’D’}=\frac{C’D’}{CD}\)

\(\frac{AB}{CD}=\frac{A’B’}{C’D’}\)

\(\frac{BC}{A’D’}=\frac{B’C’}{AD}\)

### Problem 2

Lines \(BC\) and \(DE\) are both vertical. What is the length of \(AD\)?

### Problem 3

The quilt is made of squares with diagonals. Side length \(AB\) is 2.

- What is the length of \(BD\)?
- What is the area of triangle \(AEH\)?

### Problem 4

Segment \(A’B’\) is parallel to segment \(AB\). What is the length of segment \(BB'\)?

3.5

4

10

10.5

### Problem 5

Elena thinks length \(BC\) is 16.5 units. Lin thinks the length of \(BC\) is 17.1 units. Do you agree with either of them? Explain or show your reasoning.

### Problem 6

Mai thinks knowing the measures of 2 sides is enough to show triangle similarity. Do you agree? Explain or show your reasoning.

### Problem 7

Line \(g\) is dilated with a center of dilation at \(A\). The image is line \(f\). Approximate the scale factor.