1. 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

2. Examples
Not Polygons
Polygons

3. 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

4. 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

5. 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

6. 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.

7. Draw all axes of symmetry on each figure

8. 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.

9. How many times does each figure have rotational symmetry?

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

11. 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: