# Lesson 11

Splitting Triangle Sides with Dilation, Part 2

- Let’s investigate parallel segments in triangles.

### Problem 1

Segment \(A’B’\) is parallel to segment \(AB\).

- What is the length of segment \(AB\)?
- 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 \(BC\).

- What is the area of triangle \(ABC\)?
- What is the area of triangle \(DEC\)?
- Does the scale factor for the side lengths apply to the area as well?

### Problem 4

Which of these statements is true?

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

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

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

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

### Problem 5

- Are triangles \(ABC\) and \(DEF\) similar? Show or explain your reasoning.
- If possible, find the length of \(EF\). If not, explain why the length of \(EF\) cannot be determined.

### Problem 6

What is the length of segment \(DF\)?

### 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.

\(\frac12\)

\(\frac89\)

1

\(\frac32\)

2