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Date: ______________ Math 9/9H

Date: ______________ Math 9/9H. 7.6 Rotations and Rotational Symmetry A shape has rotational symmetry when it coincides (matches) itself after a rotation of less than 360° about its centre

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Date: ______________ Math 9/9H

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  1. Date: ______________ Math 9/9H 7.6 Rotations and Rotational Symmetry A shape has rotational symmetry when it coincides (matches) itself after a rotation of less than 360° about its centre • The number of times the shape coincides (matches) with itself during a rotation of 360° is called the order of rotation • In general, for rotational symmetry, we say angle of rotational symmetry = 360°______ the order of rotation • A shape cannot have rotational symmetry of order 1

  2. Date: ______________ Math 9/9H Example 1: Identifying Shapes with Rotational Symmetry Determine which hexagons have rotational symmetry, and state the order of rotation and angle of rotational symmetry For each hexagon: • Join one vertex to the centre dot • Trace (or move) the hexagon • Rotate the tracing about the centre dot and record the order of rotation • Calculate the angle of rotation symmetry

  3. Date: ______________ Math 9/9H • The order of rotation is 3. The angle of rotation symmetry is 360°/3 = 120° B) The order of rotation is 2. The angle of rotation symmetry is 360°/2 = 180° C) This hexagon is rotated one complete turn before it coincides with itself. It does not have rotational symmetry.

  4. Date: ______________ Math 9/9H A rotation is another type of transformation. We use square grid paper to draw rotation images after a rotation of 90°, or any multiple of 90° (such as 180°, 270°, 360°, etc.). We use isometric dot paper to draw rotation images after a rotation of 60°, or any multiple of 60° (such as 120°, 180°, etc.).

  5. Date: ______________ Math 9/9H Example 2: Drawing Rotation Images Rotate Pentagon ABCDE 90° clockwise around vertex E. • Trace the shape and label the vertices on the tracing. Rotate pentagon ABCED 90° clockwise around E. Draw and label the rotation image.

  6. Date: ______________ Math 9/9H Rotate Trapezoid FGHJ 120° counterclockwise around vertex F. • Trace the shape and label the vertices on the tracing. Rotate trapezoid 120° counterclockwise around F. Draw and label the rotation image.

  7. Date: ______________ Math 9/9H Example 3: Identifying Symmetry after Rotations Rotate rectangle ABCD • 90° clockwise about vertex A • 180° clockwise about vertex A • 270° clockwise about vertex A Draw and label each rotation image. Then look at the shape formed by the rectangle and all its images, and identify any rotational symmetry in this shape.

  8. Date: ______________ Math 9/9H Trace the shape and label the vertices on the tracing. Rotate rectangle for each step, then draw and label the rotation image. 90° clockwise about vertex A – the rotation image is AEFG 180° clockwise about vertex A – the rotation image is AHJK 270° clockwise about vertex A – the rotation image is AMNP The resulting shape BCDEFGHJKMNP has rotational symmetry of order 4 about point A.

  9. Date: ______________ Math 9/9H Please complete p. 365 # 4-10, 13, 14

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