Splitting Triangle Sides with Dilation, Part 1

ID: damik-dasih
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

Splitting Triangle Sides with Dilation, Part 1

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Problem 1

1) What is the measure of angle ABCA'B'C?

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a) 20° 20 \degree b) 40° 40 \degree c) 60° 60 \degree d) 80° 80 \degree
Problem 2

2) Triangle DEFDEF is formed by connecting the midpoints of the sides of triangle ABCABC. The lengths of the sides of DEFDEF are shown. What is the length of ABAB?

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Problem 3

3) Angle ABCABC is taken by a dilation with center PP and scale factor 13\frac{1}{3} to angle ABCA'B'C'. The measure of angle ABCABC is 21°21\degree. What is the measure of angle ABCA'B'C'?

Problem 4

4) Draw 2 lines that could be the image of line mm by a dilation. Label the lines nn and pp.

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Problem 5


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5) Is it possible for polygon ABCDEABCDE to be dilated to figure VWXYZVWXYZ?

True or false? Write below.

6) Explain your reasoning.

Problem 6

7) Triangle XYZXYZ is scaled and the image is XYZX'Y'Z'. Select all of the equations that could be used to solve for aa. Write each corresponding letter in the answer box and separate letters with commas.

a) 85=3a\frac{8}{5} = \frac{3}{a} \quad\quad b) 58=3a\frac{5}{8} = \frac{3}{a} \quad\quad c) 83=5a\frac{8}{3} = \frac{5}{a} \quad\quad d) 38=5a\frac{3}{8} = \frac{5}{a} \quad\quad e) 8a=53\frac{8}{a} = \frac{5}{3}

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Problem 7

8) Lin is using the diagram to prove the statement, “If a parallelogram has one right angle, it is a rectangle.” Given that EFGHEFGH is a parallelogram and angle HEFHEF is a right angle, write a statement that will help prove angle FGHFGH is also a right angle.

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9) Han then states that the 2 triangles created by diagonal EGEG must be congruent. Help Han write a proof that triangle EHGEHG is congruent to triangle GFEGFE.