# Lesson 11

Splitting Triangle Sides with Dilation, Part 2

### Problem 1

Segment $$A’B’$$ is parallel to segment $$AB$$.

1. What is the length of segment $$AB$$?
2. What is the length of segment $$B’B$$?

### Problem 2

Explain how you know that segment $$DE$$ is not parallel to segment $$BC$$.

### Problem 3

In right triangle $$ABC$$, $$AC=4$$ and $$BC=5$$. A new triangle $$DEC$$ is formed by connecting the midpoints of $$AC$$ and $$BC$$.

1. What is the area of triangle $$ABC$$?
2. What is the area of triangle $$DEC$$?
3. Does the scale factor for the side lengths apply to the area as well?

### Problem 4

Which of these statements is true?

A:

To know whether 2 triangles are similar, it is enough to know the measure of 1 angle.

B:

To know whether 2 triangles are similar, it is enough to know the length of 1 side.

C:

To know whether 2 triangles are similar, it is enough to know the measure of 2 angles in each triangle.

D:

To know whether 2 triangles are similar, it is enough to know the measure of 2 sides in each triangle.

### Solution

(From Unit 3, Lesson 10.)

### Problem 5

1. Are triangles $$ABC$$ and $$DEF$$ similar? Show or explain your reasoning.
2. If possible, find the length of $$EF$$. If not, explain why the length of $$EF$$ cannot be determined.

### Solution

(From Unit 3, Lesson 10.)

### Problem 6

What is the length of segment $$DF$$?

### Solution

(From Unit 3, Lesson 9.)

### Problem 7

The triangle $$ABC$$ is taken to triangle $$A’B’C’$$ by a dilation. Select all of the scale factors for the dilation that would result in an image that was smaller than the original figure.

A:

$$\frac12$$

B:

$$\frac89$$

C:

1

D:

$$\frac32$$

E:

2