# Splitting Triangle Sides with Dilation, Part 2

13 questions

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