# Lesson 4Cut by a TransversalSolidify Understanding

Solve for to find the missing side in each right triangle.

### 4.

Create a proportion for each set of similar triangles that can be used to find the missing side length indicated. Then solve the proportion.

## Set

### 7.

Jack and Diane are designing a trellis for some special plants they are planning to put in their backyard garden. Use the values provided on the sketch of the trellis to find the missing values for , , and .

### 8.

Use the diagram to prove .

### 9.

Write and solve a proportion that will provide the missing length.

### 10.

Write and solve a proportion that will provide the missing length.

For problems 11–14, find the parallel line segments in the diagram and write a mathematical statement showing the parallel line segments. Then write a similarity statement for the triangles that are similar (i.e. ). Explain why those triangles would be similar.