Lesson 21: Line of Symmetry and Rotational Symmetry

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1 Lesson 21: Line of Symmetry and Rotational Symmetry Warmup 1. A(1, 6), B(4, 7), C(1, 3) R O,90 r x axis ( ABC) A B C A B C 2. Using the rules, determine the coordinates of the missing point. a) O,90 R ( 6,4) (, ) b) rx 0 ( 3, 5) (, ) c) O,270 R (, ) ( 3, 4) d) r (7, 8) (, ) x axis e) ry axis (, ) (8,4) f) RO, 270 ( 5, 8) (, ) i) T 5,2 (4, 2) = (, ) j) r y=x (1, 5) = (, )

2 Lesson 21: Line of Symmetry and Rotational Symmetry Learning Targets: I can draw the lines of symmetry for a given figure I can identify rotational symmetry within an individual figure. Lesson 21 M1 Definitions 1. occurs when two halves of the figure are mirror images of each other when reflected across a line. 2. The of is the line which divides the figure into two mirror images. Process To determine if a figure has a line of symmetry, fold the figure along the supposed line of symmetry to see if the two halves coincide. A figure has a line of symmetry if the figure can be mapped onto itself by a reflection in the line. Directions: Watch your teacher as s(he) folds each shape to show if the lines that divide the figures in halves are actually the lines of symmetry Square Isosceles Rectangle Example 1) Determine the number of lines of symmetry for each of the following figures and draw them.

3 Not all lines that divide a figure into two congruent halves are lines of symmetry. The diagonal of a rectangle divides the rectangle into two triangles that are congruent (same size and shape). The diagonal of a parallelogram also divides the figure into two triangles that are congruent. Rotational Symmetry of a Figure: Rotational symmetry of a figure is a rotation of the plane that maps the figure back to itself such that the angle of rotation is greater than but less than. **Another word for this rotational symmetry is the symmetry. Which of the polygons above only has identity symmetry?

4 Degree of Rotational Symmetry If a figure can be rotated degrees and map onto itself, it has symmetry. The number of rotated positions in which the object looks exactly the same is the of the rotational symmetry. To calculate the lowest degree of rotational symmetry divide: All other degrees of rotational symmetry are multiples of that value up to and including 360 o. When determining order, the last rotation returns the object to its original position (360). The angles of 0 and 360 are not listed as they are the starting locations. Order 1 implies no true rotational symmetry exists, since a full 360 degree rotation is needed to again display the object with its original appearance. Order 2 implies a duplicate image at a rotation of 180 (divide 360 into 2 equal parts). Order 3 implies a duplicate image at 120 and 240 (divide 360 into 3 equal parts). Order 4 implies a duplicate image at 90, 180, and 270 (divide 360 into 4 equal parts). What is the order of symmetry and the degrees of rotational symmetry for the last 2 figures; flower and the crop circle? Flower: Crop Circle:

5 Example 2) Triangle ABC given below is equilateral. a) What 3 types of symmetry does ABC have? b) What is the order of symmetry? What are the degrees of rotational symmetry of ABC? c) Use your compass to construct two lines of symmetry for ABC. (Connections: A figure has Lines of Symmetry if a perpendicular bisector or angle bisector separates the figure into its own mirror images) d) Label the point of intersection as D, which is the center of rotational symmetry for ABC.

6 Lesson 21: Line of Symmetry and Rotational Symmetry Work Time / Problem Set ABCDE is a regular pentagon. Use the drawing to answer #1-3. A Figure 1 B Problem 1) Draw all lines of symmetry. Locate the center of rotational symmetry. a) What are the degrees of rotational symmetry? E C b) What is the order of the rotational symmetry? D Problem 2) a) Identify the capital letters given that have line(s) of symmetry b) Identify all capital letters that have rotational symmetry. Problem 3) State the lowest degree of rotational symmetry for each figure: Problem 4) Use Figure 3 at right to answer problem 4. a) Draw all lines of symmetry. Locate the center of rotational symmetry. b) What are the degrees of rotational symmetry? c) What is the order of the rotational symmetry? d) What is the total number of symmetries for the figure? e) Shade the figure so that the resulting figure only has 3 possible rotational symmetries (including the identity symmetry). Figure 3

7 Problem 5) Give the order of rotational symmetry and the degrees of rotational symmetry.

8 Pictures to be used to show reflection symmetry and lines of symmetry for smart notebook

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