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Geometry 9-4 Compositions of Isometries
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by Matthew Richardson
| 24 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.
The outlined content above was added from outside of Formative.
The outlined content above was added from outside of Formative.
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1
10 pts
Solve It! The blue E is a horizontal translation of the red E. How can you use two reflections, one right after the other, to move the red E to the position of the blue E?
2
10 pts
Solve It! Draw the two lines of reflection you used on the image on the canvas.
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3
10 pts
Problem 1 Got It? Lines l and m are copied from Problem 1. Draw J between l and m. Draw the image of the following composition of reflections in blue or green.

4
10 pts
Problem 1 Got It? What is the distance of the resulting translation in the previous item?
5
10 pts
Problem 1 Got It? Reasoning: Use the results of the previous items and Problem 1. Make a conjecture about the distance of any translation that is the result of a composition of reflections across two parallel lines.
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6
10 pts
Problem 2 Got It? Draw the following composition of reflections on the canvas.
7
10 pts
Problem 2 Got It? What is the center for the resulting rotation?
a
b
C
8
10 pts
Problem 2 Got It? What is the angle of rotation for the resulting rotation?
45° clockwise
90° clockwise
180° clockwise
9
10 pts
Problem 2 Got It? Reasoning: Use the results of the previous items and Problem 2. Make a conjecture about the center of rotation and the angle of rotation for any rotation that is the result of any composition of reflections across two intersecting lines.
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10
10 pts
Problem 3 Got It? Graph ΔTEX in black. Graph the image ΔT'E'X' for the glide reflection in green or blue. Be sure to include relevant graph detail.

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11
20 pts
For each diagram, sketch the image of Z reflected across line a, then across line b. Use green or blue.
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12
10 pts
A
B
C
D
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14
10 pts
Error Analysis: You reflect ∆DEF first across line m and then across line n. Your friend says you can get the same result by reflecting ∆DEF first across line n and then across line m. Explain your friend's error.
15
10 pts
Review Lesson 9-3: Draw ∆ABC in black and its image for the rotation described in blue or green. Label all vertices.

16
10 pts
Review Lesson 9-3: Draw ∆ABC in black and its image for the rotation described in blue or green. Label all vertices.

17
10 pts
Review Lesson 5-5: Identify the two statements that contradict each other.
  • Statements that contradict each other
    Answer by dragging items here
18
10 pts
Review Lesson 5-5: Identify the two statements that contradict each other.
  • Statements that contradict each other
    Answer by dragging items here
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19
10 pts
Review Lesson 4-2: Determine whether the triangles in each pair must be congruent. If so, name the postulate of theorem that justifies your answer.
  • Not necessarily congruent
    Answer by dragging items here
  • SSS
    Answer by dragging items here
  • ASA
    Answer by dragging items here
20
10 pts
Vocabulary Review: Match the pairs of corresponding sides.
  • segment J'Q'
    Answer by dragging items here
  • segment JK
    Answer by dragging items here
  • segment K'Q'
    Answer by dragging items here
21
10 pts
Vocabulary Review: Complete each sentence.
  • The image of ∠J is __?__.
    Answer by dragging items here
  • The transformation △JKQ → △J'K'Q' is a __?__.
    Answer by dragging items here
22
10 pts
Use Your Vocabulary: Complete each sentence with image or preimage.
  • In a transformation, the original figure is the __?__.
    Answer by dragging items here
  • The resulting figure is the __?__.
    Answer by dragging items here
23
10 pts
Use Your Vocabulary: Which type of transformation maps each (x, y) to (x - 8, y + 2)?
translation
reflection
rotation
glide reflection
dilation
24
10 pts
Reflection: Math Success
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