Polygons and Symmetry Goals: Define a Polygon Define and Use reflectional symmetry and rotational symmetry Define regular polygon and use the central angle theorem of a regular polygon

Examples Not Polygons Polygons

Vocab Term Picture Definition Polygon Sides of a Polygon Vertices of a Polygon A closed plane figure formed by three or more segments such that each intersect exactly two other segments. Segments of a polygon The common endpoints of those segments

All sides are congruent Term Picture Definition Equiangular Polygon Equilateral Polygon Regular Polygon Central Angle All angles congruent All sides are congruent Both equiangular and equilateral An angle whose vertex is the center of the polygon and whose sides pass through two consecutive vertices

Polygons Classified by Number of Sides Name of Polygon 3  triangle 9  nonagon 4 quadrilateral 10  decagon 5  pentagon 11  11-gon or hendecagon 6  hexagon 12  dodecagon 7  heptagon 13  13-gon 8  octagon n  n-gon

Reflectional Symmetry: A figure has reflectional symmetry if and only if its reflected image across a line coincides exactly with the preimage, the original figure. Axis of Symmetry: A line that divides a figure into two congruent reflected halves.

Draw all axes of symmetry on each figure

Rotational Symmetry: A figure has rotational symmetry if and only if it has at least one rotation image not counting rotation images of 0º or multiples of 360º, that coincide with the original figure.

How many times does each figure have rotational symmetry?

Activity with Patty Paper… The measure of a central angle of a regular polygon with n sides is given by the following formula: ___________________________

Example 1: Find the measure of the central angle of each regular polygon below: a) decagon b) heptagon c) 15-gon Measure of central angle: Measure of central angle: Measure of central angle: