Pearson Unit 2 Topic 8: Transformational Geometry 8-4: Symmetry Pearson Texas Geometry ©2016 Holt Geometry Texas ©2007

TEKS Focus: (3)(D) Identify and distinguish between reflectional and rotational symmetry in a plane figure. (1)(C) Select tools, including real objects, manipulatives paper and pencil, and technology as appropriate, and techniques, including mental math, estimations, and number sense as appropriate, to solve problems. (1)(D) Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate. (1)(E) Create and use representations to organize, record, and communicate mathematical ideas.

Example #1LINE SYMMETRY Which capital letters have horizontal line symmetry? B C D E H I K O X Which capital letters have vertical line symmetry? A H I M O T U V W X Y

Example #2 MORE LINE SYMMETRY How many lines of symmetry do regular polygons have? Write a rule using n as the number of sides in the polygon. 7 lines 8 lines 10 lines A regular polygon with n sides has n lines of symmetry.

Example #3 ROTATIONAL SYMMETRY Do the following figures have rotational symmetry? If yes, then state the degree of the angle of rotation. Assume the point of rotation is the center of the figure. Yes; 180 No Yes; 360/7 Yes; 180 No Yes; 72

Example #4 Determine if these figures appear to have reflectional symmetry, rotational symmetry (with degree), neither, or both. Both kinds: 8 lines of reflection and 45 of rotational symmetry. Only 1 line of vertical reflection. No symmetry.

Example #5 Graphing Parabolas Graph the following parabolas and determine the equation of the line of symmetry: 𝑓(𝑥)= (𝑥+3) 2 and g(x)= (𝑥−1) 2 Also determine what makes the parabola move to the left or right of the origin. Line of symmetry is x = -3 Line of symmetry is x = 1 The h in the vertex form controls the horizontal shift. The k in the vertex form controls the vertical shift.