LESSON 9–5 Symmetry

Five-Minute Check (over Lesson 9–4) TEKS 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 Key Concept: Three-Dimensional Symmetries Example 3: Three-Dimensional Symmetry Lesson Menu

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

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

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

Mathematical Processes G.1(E), G.1(F) Targeted TEKS G.3(D) Identify and distinguish between reflectional and rotational symmetry in a plane figure. Mathematical Processes G.1(E), G.1(F) TEKS

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

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

Concept

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, draw all lines of symmetry, and state their number. Answer: yes; 7 lines of symmetry Example 1

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

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, draw all lines of symmetry, and state their number. Answer: yes; 5 lines of symmetry Example 1

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

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

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

Concept

Identify Rotational Symmetry A. State whether the figure has rotational symmetry. Write yes or no. If so, 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

Identify Rotational Symmetry B. State whether the figure has rotational symmetry. Write yes or no. If so, 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

Identify Rotational Symmetry C. State whether the figure has rotational symmetry. Write yes or no. If so, 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

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

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

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

Concept

Answer: both plane and axis symmetry Three-Dimensional Symmetry A. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: both plane and axis symmetry Example 3

Answer: neither plane nor axis symmetry Three-Dimensional Symmetry B. State whether the figure has plane symmetry, axis symmetry, both, or neither. Answer: neither plane nor axis symmetry Example 3

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

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

LESSON 9–5 Symmetry