9.5 symmetry 2017 ink.notebook. October 25, Page Symmetry Page 134. Standards. Page Symmetry. Lesson Objectives.

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1 9.5 symmetry 2017 ink.notebook Page Symmetry Page 134 Lesson Objectives Standards Lesson Notes Page Symmetry Press the tabs to view details. 1

2 Lesson Objectives Press the tabs to view details. Standards Lesson Notes After this lesson, you should be able to successfully be able to determine the type of symmetry and the magnitude of symmetry. Lesson Objectives Standards Lesson Notes G.CO.2 Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch). G.CO.3 Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G.CO.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G.CO.5 Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G.CO.6 Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent. Press the tabs to view details. Symmetry In Two Dimensional Figures Line Symmetry or symmetry: a figure has line symmetry if the figure can be mapped onto itself by a reflection line called the. Some figures have no line of symmetry, some have only one, and some have two or more of lines of symmetry 2

3 Rotational Symmetry: The figure below has rotational symmetry because it MAPPED onto itself before it is completely turned around a point. A figure in a plane has if the figure can be mapped onto itself by a rotation between 0 and 360 about the center of the figure, called the center of symmetry. The number of times a figure maps onto itself as it rotates from 0 to 360 is called the ORDER OF SYMMETRY. The magnitude of symmetry or ANGLE of rotation is the smallest angle through which a figure can be rotated so that it maps onto itself. Magnitude = 360 order EXAMPLE 1: The heart has line symmetry. It has one line of symmetry. State whether the figure appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry and state their number

4 9.5 symmetry 2017 ink.notebook EXAMPLE 2: The figure has rotational symmetry. It has order 4 symmetry and a magnitude of or 90 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 Symmetry In Three Dimensional Figures A three dimensional figure has if the figure can be mapped onto itself by a reflection in a plane. A three dimensional figure has if the figure can be mapped onto itself by a rotation between 0 and 360 in a line. 4

5 a) The cylinder has plane symmetry. The cylinder has axis symmetry. b) The letter N has plane symmetry. Example: State whether the figure has plane symmetry, axis symmetry, both, or neither

6 PRACTICE On the Worksheet 9.5 Practice State whether the figure appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry and state their number Practice State whether the figure appears to have line symmetry. Write yes or no. If so, draw all lines of symmetry and state their number

7 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 LETTERS Examine each capital letter in the alphabet. Determine which letters have 180 rotational symmetry about a point in the center of the letter. 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 Example: State whether the figure has plane symmetry, axis symmetry, both, or neither

8 19. STEAMBOATS A paddle wheel on a steamboat is driven by a steam engine that rotates the paddles attached to the wheel to propel the boat through the water. If a paddle wheel consists of 18 evenly spaced paddles, identify the order and magnitude of its rotational symmetry. 20. POLYGONS A regular polygon has rotational symmetry with an order of 5 and a magnitude of 72. What is the figure? 21. Explain order and magnitude of symmetry. Answers: Answers: 1. Yes, 3 3. Yes, 2 5. No 7. Yes, 2 9. Yes, H, I, N, O, S, X, Z 13 yes, 8, neither 17. Both , Order is # of times a figure rotates onto itself yes, 3 yes, 2 5. no 7. yes, 2 8

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