POLYGONS
AND
SYMMETRY
Goals:
•Define a Polygon
•Define
•Define
and Use reflectional symmetry and rotational symmetry
regular polygon and use the central angle theorem of a
regular polygon
EXAMPLES
Polygons
Not Polygons
VOCAB
Term
Picture
Definition
Polygon
A closed plane figure
formed by three or
more segments such
that each intersect
exactly two other
segments.
Sides of a Polygon
Segments of a polygon
Vertices of a Polygon
The common
endpoints of those
segments
Term
Equiangular Polygon
Equilateral Polygon
Regular Polygon
Central Angle
Picture
Definition
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
#
sides
Name of Polygon
#
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: