2.4 Symmetry Key concepts: Lines of symmetry Rotational Symmetry

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Presentation transcript:

2.4 Symmetry Key concepts: Lines of symmetry Rotational Symmetry Degree of rotational symmetry

Vocabulary Mapping – a shape is said to be “mapped” onto itself if a series of transformations causes one shape to EXACTLY occupy the size, shape, and position of another shape.

Definitions A figure has symmetry if 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

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

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

Definitions ROTATIONAL SYMMETRY: If a figure can be rotated less than 360° about its center so that the image and the preimage are indistinguishable, the figure has rotational symmetry. p. 664

Definitions Degree of Rotational 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.

Identify Rotational Symmetry A. State whether the figure has rotational 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.

B. State whether the figure has rotational symmetry. Answer: The propeller has order 3 rotational symmetry and magnitude 360 ÷ 3 = 120°. The center of the propeller is the center of rotation.

C. State whether the figure has rotational symmetry. Answer: The gear has order 8 rotational symmetry and magnitude 360 ÷ 8 = 45°. The center of the gear is the center of rotation.

A. State whether the figure has rotational symmetry A. State whether the figure has rotational symmetry. If so, state the degree of rotational of symmetry. A. Yes, 45° B. Yes, 90° C. Yes, 180° D. No, the figure does not have rotational symmetry.

B. State whether the figure has rotational symmetry. A. Yes, 45° B. Yes, 60° C. Yes, 90° D. No, the figure does not have rotational symmetry.

C. State whether the figure has rotational symmetry. A. Yes, 90° B. Yes, 90° C. Yes, 180° D. No, the figure does not have rotational symmetry.

Homework: Page 106, #’s 1-6 and 9-11 For 9-11, ignore directions and state whether the transformation given causes the figure to be mapped onto itself.