Splitting Triangle Sides with Dilation, Part 2

ID: hitik-lilap
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Splitting Triangle Sides with Dilation, Part 2

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Problem 1

Segment ABA'B' is parallel to segment ABAB.

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1) What is the length of segment ABAB?

2) What is the length of segment BBB'B?

Problem 2

3) Explain how you know that segment DEDE is not parallel to segment BCBC.

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Problem 3

In right triangle ABCABC, AC=4AC = 4 and BC=5BC = 5. A new triangle DECDEC is formed by connecting the midpoints of ACAC and BCBC.

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4) What is the area of triangle ABCABC?

5) What is the area of triangle DECDEC?

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) To know whether 2 triangles are similar, it is enough to know the measure of 1 angle.\text{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.\text{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.\text{To know whether 2 triangles are similar, it is enough to know the measure of 2 angles } \newline \text{ in each triangle.}d) To know whether 2 triangles are similar, it is enough to know the measure of 2 sides  in each triangle.\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


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9) Are triangles ABCABC and DEFDEF similar?

True or false? Write below.

10) Show or explain your reasoning.

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

Problem 6

12) What is the length of segment DFDF?

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Problem 7

13) The triangle ABCABC is taken to triangle ABCA'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) 12\frac{1}{2} \quad\quad b) 89\frac{8}{9} \quad\quad c) 1 \quad\quad d) 32\frac{3}{2} \quad\quad e) 2