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**9-5 Symmetry 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.

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Definitions A figure has symmetry is there exists a rigid motion (reflection, translation, rotation, or glide reflection that maps the figures unto itself. Line of symmetry is a line that can be drawn through a plane figure so that the figure on one side is the reflection image of the figure on the opposite side. It can also be referred to axis of symmetry. A figure has line symmetry (or reflection symmetry) if the figure can be mapped onto itself by a reflection in a line of symmetry. p. 663

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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

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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

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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

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**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

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**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

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**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

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Definitions If a figure can be rotated less than 360° about a point so that the image and the preimage are indistinguishable, the figure has rotational symmetry. Point of symmetry – a figure that can be mapped onto itself by a rotation of 180°. It is also known as center of symmetry. p. 664

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**Definitions Magnitude = 360°÷ order**

Order of symmetry – the number of times a figure maps onto itself as it rotates from 0° to 360°. The magnitude of symmetry – the smallest angle through which a figure can be rotated so that it maps onto itself. It can also be called the angle of rotation. The order and magnitude of a rotation are related by: Magnitude = 360°÷ order

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**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.

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**B. State whether the figure has rotational symmetry. Write yes or no**

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.

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**C. State whether the figure has rotational symmetry. Write yes or no**

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.

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**A. State whether the figure has rotational symmetry**

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.

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**B. State whether the figure has rotational symmetry**

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.

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**C. State whether the figure has rotational symmetry**

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.

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p. 665

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**A. State whether the figure has plane symmetry, axis symmetry, both, or neither.**

Answer: both plane and axis symmetry

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**B. State whether the figure has plane symmetry, axis symmetry, both, or neither.**

Answer: neither plane nor axis symmetry

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**A. State whether the figure has plane symmetry, axis symmetry, both or neither.**

A. plane symmetry B. axis symmetry C. both D. neither

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**B. State whether the figure has plane symmetry, axis symmetry, both or neither.**

A. plane symmetry B. axis symmetry C. both D. neither

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9-5 Assignment Page 666, even

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