One Hundred and Eighty

ID: kufin-golij
Illustrative Mathematics
Subject: Geometry

17 questions

One Hundred and Eighty

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Problem 1

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

1) Which triangles are translations of triangle 1?

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

2) Explain how you know.

3) Which triangles are not translations of triangle 1?

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

4) Explain how you know.

Problem 2

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

5) Angle 1:

6) Angle 2:

7) Angle 3:

Problem 3

8) In the figure shown, lines ﻿$f$﻿ and ﻿$g$﻿ are parallel. Select the angle that is congruent to angle 1.

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

9) Angle ﻿$BDE$﻿ is congruent to angle ﻿$BAC$﻿. Name another pair of congruent angles.

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 ﻿$AD$﻿ and ﻿$EC$﻿ meet at point ﻿$B$﻿.

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 ﻿$B$﻿ takes ﻿$D$﻿ to ﻿$A$﻿.

b) The image of ﻿$D$﻿ after a 180 degree rotation using center ﻿$B$﻿ lies on ray ﻿$BA$﻿.

c) If a 180 degree rotation using center ﻿$B$﻿ takes ﻿$C$﻿ to ﻿$E$﻿ then it also takes ﻿$E$﻿ to ﻿$C$﻿.

d) Angle ﻿$ABC$﻿ is congruent to angle ﻿$DBE$﻿. e) Angle ﻿$ABE$﻿ is congruent to angle ﻿$ABC$﻿.

Problem 7

14) Points ﻿$E$﻿, ﻿$B$﻿, and ﻿$C$﻿ are collinear. Explain why points ﻿$A$﻿, ﻿$B$﻿, and ﻿$D$﻿ are collinear.

Problem 8

15) Draw the image of figure ﻿$ACTS$﻿ after a clockwise rotation around point ﻿$C$﻿ using angle ﻿$CTS$﻿ and then a translation by the directed line segment ﻿$CT$﻿.

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

Problem 9

17) Triangle ﻿$ABC$﻿ is congruent to triangle ﻿$A'B'C'$﻿. Describe a sequence of rigid motions that takes ﻿$A$﻿ to ﻿$A'$﻿, ﻿$B$﻿ to ﻿$B'$﻿, and ﻿$C$﻿ to ﻿$C'$﻿.