One Hundred and Eighty

ID: kufin-golij
Created by Illustrative MathIllustrative Math
Subject: Geometry
Grade: 9-12

One Hundred and Eighty

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Problem 1

The triangles here are each obtained by applying rigid motions to triangle 1.

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1) Which triangles are translations of triangle 1?

a) The even numbered triangles\text{The even numbered triangles}b) The odd numbered triangles\text{The odd numbered triangles}c) All of the triangles\text{All of the triangles}d) None of the triangles\text{None of the triangles}

2) Explain how you know.

3) Which triangles are not translations of triangle 1?

a) The even numbered triangles\text{The even numbered triangles}b) The odd numbered triangles\text{The odd numbered triangles}c) All of the triangles\text{All of the triangles}d) None of the triangles\text{None of the triangles}

4) Explain how you know.

Problem 2

The quadrilateral is a parallelogram. Find the measure of angles 1, 2, and 3.

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5) Angle 1:

6) Angle 2:

7) Angle 3:

Problem 3

8) In the figure shown, lines ff and gg are parallel. Select the angle that is congruent to angle 1.

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a) Angle 2\text{Angle 2}b) Angle 6 \text{Angle 6 }c) Angle 7 \text{Angle 7 }d) Angle 8\text{Angle 8}
Problem 4

9) Angle BDEBDE is congruent to angle BACBAC. Name another pair of congruent angles.

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10) Explain how you know.

Problem 5

11) Describe a transformation that could be used to show that corresponding angles are congruent.

12) Describe a transformation that could be used to show that alternate interior angles are congruent.

Problem 6

13) Lines ADAD and ECEC meet at point BB.

Which of these must be true? Select all that apply. Write each corresponding letter in the answer box and separate letters with commas.

a) A 180 degree clockwise rotation using center BB takes DD to AA.

b) The image of DD after a 180 degree rotation using center BB lies on ray BABA.

c) If a 180 degree rotation using center BB takes CC to EE then it also takes EE to CC.

d) Angle ABCABC is congruent to angle DBEDBE. \quad\quad e) Angle ABEABE is congruent to angle ABCABC.

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Problem 7

14) Points EE, BB, and CC are collinear. Explain why points AA, BB, and DD are collinear.

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Problem 8

15) Draw the image of figure ACTSACTS after a clockwise rotation around point CC using angle CTSCTS and then a translation by the directed line segment CTCT.

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16) Describe another sequence of transformations that will result in the same image.

Problem 9

17) Triangle ABCABC is congruent to triangle ABCA'B'C'. Describe a sequence of rigid motions that takes AA to AA', BB to BB', and CC to CC'.

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