# Splitting Triangle Sides with Dilation, Part 2

# 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

3) 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 $BC$.

4) What is the area of triangle $ABC$?

5) What is the area of triangle $DEC$?

6) Does the scale factor for the side lengths apply to the area as well?

7) If not, what is the ratio of the areas?

##### Problem 4

8) Which of these statements is true?

##### Problem 5

9) Are triangles $ABC$ and $DEF$ similar?

10) Show or explain your reasoning.

11) If possible, find the length of $EF$. If not, explain why the length of $EF$ cannot be determined.

##### Problem 6

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

##### Problem 7

13) 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. Write each corresponding letter in the answer box and separate letters with commas.

a) $\frac{1}{2}$ $\quad\quad$ b) $\frac{8}{9}$ $\quad\quad$ c) 1 $\quad\quad$ d) $\frac{3}{2}$ $\quad\quad$ e) 2