1. Five-Minute Check (over Lesson 3–4) Mathematical Practices Then/Now
New Vocabulary
Key Concept: Line Symmetry
Example 1: Real-World Example: Identify Line Symmetry
Key Concept: Rotational Symmetry
Example 2: Identify Rotational Symmetry
Example 3: Describe Reflections and Rotations
Lesson Menu

2. Triangle XYZ has vertices X(–3, 1), Y(–4, 5), and Z(0, 5)
Triangle XYZ has vertices X(–3, 1), Y(–4, 5), and Z(0, 5). Graph ΔXYZ and its image after the indicated glide reflection. Translation: along 5, –2, Reflection: in x-axis
A. B.
C. D.
5-Minute Check 1

3. Triangle XYZ has vertices X(–3, 1), Y(–4, 5), and Z(0, 5)
Triangle XYZ has vertices X(–3, 1), Y(–4, 5), and Z(0, 5). Graph ΔXYZ and its image after the indicated glide reflection. Translation: along 0, –4, Reflection: in y-axis
A. B.
C. D.
5-Minute Check 2

4. Which of the following characteristics is not preserved under a glide reflection?
A. length
B. angle measure
C. orientation
D. parallel lines
5-Minute Check 3

5. Mathematical Practices 4 Model with mathematics.
8 Look for and express regularity in repeated reasoning.
Content Standards
G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. MP

6. You drew reflections and rotations of figures.
Identify line and rotational symmetries in two-dimensional figures.
Identify line and rotational symmetries in three-dimensional figures.
Then/Now

7. symmetry line symmetry line of symmetry rotational symmetry
center of symmetry
order of symmetry
magnitude of symmetry
plane symmetry
axis symmetry
Vocabulary

8. Concept

9. Answer: yes; 7 lines of symmetry
Identify Line Symmetry
A. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number.
Answer: yes; 7 lines of symmetry
Example 1

10. Identify Line Symmetry
B. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number.
Answer: no
Example 1

11. Answer: yes; 5 lines of symmetry
Identify Line Symmetry
C. KALEIDOSCOPES State whether the object appears to have line symmetry. Write yes or no. If so, copy the figure, draw all lines of symmetry, and state their number.
Answer: yes; 5 lines of symmetry
Example 1

12. A. State whether the figure appears to have line symmetry
A. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number.
A. yes; 1 line
B. yes; 2 lines
C. yes; 3 lines
D. no
Example 1

13. B. State whether the figure appears to have line symmetry
B. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number.
A. yes; 1 line
B. yes; 2 lines
C. yes; 4 lines
D. no
Example 1

14. C. State whether the figure appears to have line symmetry
C. State whether the figure appears to have line symmetry. Write yes or no. If so, state their number.
A. yes; 1 line
B. yes; 2 lines
C. yes; 4 lines
D. no
Example 1

15. Concept

16. Identify Rotational Symmetry
A. State whether the figure has rotational symmetry. Write yes or no. If so, copy the figure, locate the center of symmetry, and state the order and magnitude of symmetry.
Answer: Yes the star has order 5 rotatonal symmetry and magnitude 360 ÷ 5 = 72°. The center of the star is the center of rotation.
Example 2

17. Identify Rotational Symmetry
B. State whether the figure has rotational symmetry. Write yes or no. If so, copy the figure, locate the center of symmetry, and state the order and magnitude of symmetry.
Answer: The propeller has order 3 rotational symmetry and magnitude 360 ÷ 3 = 120°. The center of the propeller is the center of rotation.
Example 2

18. Identify Rotational Symmetry
C. State whether the figure has rotational symmetry. Write yes or no. If so, copy the figure, locate the center of symmetry, and state the order and magnitude of symmetry.
Answer: The gear has order 8 rotational symmetry and magnitude 360 ÷ 8 = 45°. The center of the gear is the center of rotation.
Example 2

19. A. Yes, order 8 and magnitude 45° B. Yes, order 4 and magnitude 90°
A. State whether the figure has rotational symmetry. If so, state the order and magnitude of symmetry.
A. Yes, order 8 and magnitude 45°
B. Yes, order 4 and magnitude 90°
C. Yes, order 4 and magnitude 180°
D. No, the figure does not have rotational symmetry.
Example 2

20. A. Yes, order 8 and magnitude 45° B. Yes, order 6 and magnitude 60°
B. State whether the figure has rotational symmetry. If so, state the order and magnitude of symmetry.
A. Yes, order 8 and magnitude 45°
B. Yes, order 6 and magnitude 60°
C. Yes, order 4 and magnitude 90°
D. No, the figure does not have rotational symmetry.
Example 2

21. A. Yes, order 3 and magnitude 90° B. Yes, order 4 and magnitude 90°
C. State whether the figure has rotational symmetry. If so, state the order and magnitude of symmetry.
A. Yes, order 3 and magnitude 90°
B. Yes, order 4 and magnitude 90°
C. Yes, order 2 and magnitude 180°
D. No, the figure does not have rotational symmetry.
Example 2

22. Describe Reflections and Rotations
State whether the figure has line symmetry and/or rotational symmetry. If so, describe the reflections and/or rotations that map the figure onto itself.
Answer: line symmetry; The reflection across the line y = 2 maps the trapezoid onto itself.
Example 3

23. A. State whether the figure has plane symmetry, axis symmetry, both or neither.
A. plane symmetry
B. axis symmetry
C. both
D. neither
Example 3

24. B. State whether the figure has plane symmetry, axis symmetry, both or neither.
A. plane symmetry
B. axis symmetry
C. both
D. neither
Example 3