# Splitting Triangle Sides with Dilation, Part 2

ID: hitik-lilap
Illustrative Mathematics
Subject: Geometry

13 questions

# Splitting Triangle Sides with Dilation, Part 2

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##### 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?

True or false? Write below.

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

##### Problem 4

8) Which of these statements is true?

a) $\text{To know whether 2 triangles are similar, it is enough to know the measure of 1 angle.}$b) $\text{To know whether 2 triangles are similar, it is enough to know the length of 1 side.}$c) $\text{To know whether 2 triangles are similar, it is enough to know the measure of 2 angles } \newline \text{ in each triangle.}$d) $\text{To know whether 2 triangles are similar, it is enough to know the measure of 2 sides } \newline \text{ in each triangle.}$
##### Problem 5

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

True or false? Write below.

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