Date: Period: Symmetry

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1 Name: Date: Period: Symmetry 1) Line Symmetry: A line of symmetry not only cuts a figure in, it creates a mirror image. In order to determine if a figure has line symmetry, a figure can be divided into two mirror image halves. The line of symmetry is from all corresponding pairs of points. Another way of thinking about line symmetry is that a figure has line symmetry such that the image of the figure when reflected over the line is itself. Examples: In the figures below, sketch all the lines of symmetry (if any): More Examples: Letters and numbers can also have lines of symmetry! Sketch as many lines of symmetry as you can (if any):

2 2) Rotational Symmetry: A rotational symmetry of a figure is a rotation of the plane that maps the figure back to itself such that the rotation is greater than, but less than. In regular polygons (polygons in which all sides are congruent), the number of rotational symmetries equals the number of sides of the figure. A rotation of Symmetry) will always map a figure back onto itself! This is called the Identity Transformation (Identity Think back to Rotations: 90-turn the paper once 180-turn the paper twice 270-turn the paper three times 360-turn it all the way around (four times) Center of Rotation Determine if the following figures have Rotational Symmetry and/or Identity Symmetry.

3 3) Point Symmetry: Point symmetry is when every part of the image has a matching part that is The same distance from the central point. In the opposite direction. When an image has point symmetry, it looks the same from opposite directions, such as left vs. right, or if turned upside down. In point symmetry, the center is a to every segment formed by joining a point to its image. *A simple check to test to see if a figure has point symmetry is to turn the paper upside-down and see if it looks the same. If the figure looks the same, it has point symmetry. A figure that has point symmetry is unchanged after a 180-degree rotation. Let s notice how these all have Point Symmetry! Let s see if these figures have point symmetry! Circle the ones that do. Examples: Using regular pentagon ABCDE pictured to the right, complete the following questions: 1) Draw in all lines of symmetry. 2) Locate the center of rotational symmetry. Label this point F. 3) Is there rotational symmetry? If so, how many? 4) How many degrees of rotational symmetry does it have? 5) Does it have point symmetry?

4 Name: Symmetry Homework Date: Period: Geometry Directions: Answer the following questions completely. Make sure to show all work. 1) Which figure has one and only one line of symmetry? (a) rhombus (b) circle (c) square (d) isosceles trapezoid 2) Which type of symmetry, if any, does a square have? (a) line symmetry, only (b) both line and point symmetry (c) point symmetry (d) no symmetry 3) Which letter has both line and point symmetry? (a) Z (b) T (c) C (d) H 4) What is the total number of lines of symmetry for an equilateral triangle? (a) 1 (b) 2 (c) 3 (d) 4 5) Which letter has point symmetry but no line symmetry? (a) E (b) S (c) W (d) O 6) Which number has both horizontal and vertical line symmetry? (a) 8I8 (b) 383 (c) 414 (d) 100 7) Which letter has line symmetry but no point symmetry? (a) O (b) X (c) N (d) M 8) Which geometric shape does not have any lines of symmetry? (a) (b) (c) (d)

5 9) Using regular octagon pictured to the right, complete the following questions: a) Draw in all lines of symmetry. b) Locate the center of rotational symmetry. Label this point F. c) Is there rotational symmetry? If so, how many? d) How many degrees of rotational symmetry does it have? e) Does it have point symmetry? 10) Using the diagram pictured to the right, complete the following questions: a) Draw in all lines of symmetry. b) Locate the center of rotational symmetry. Label this point I. c) Is there rotational symmetry? If so, how many? d) How many degrees of rotational symmetry does it have? e) Does it have point symmetry? 11) Using the figure provided, shade exactly 2 of the 9 smaller squares so that the resulting figure has: 1) Only two lines of symmetry 2) No lines of symmetry about the diagonals.

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