1. Polygons and Angles
Sec 12 -1E pg

2. Definition
Polygon – a simple, closed figure formed by three or more straight line segments.
A polygon is named by the letters of its vertices, written in consecutive order.
Not
Polygons
Polygons

3. Polygons – or Not? Polygons have Not Polygons
Line segments are called sides
Sides meet only at their endpoints
Points of intersection are called vertices
Not Polygons
Figures have sides that cross each other
Figures are open
Figures have curved sides.
Not
Polygons
Polygons

4. Regular Polygons An equilateral polygon has all sides congruent.
A polygon is equiangular if all of its angles are congruent.
A regular polygon is equilateral and equiangular with all sides and all angles congruent.

5. Names of Polygons Number of Sides Name 3 Triangle 4 Quadrilateral 56 7 8 9 10 12
n sides
Name
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
Dodecagon
n-gon
An 11 sided polygon is sometimes referred to as a
undecagon or a hendecagon

6. Interior Angle Sum of a Polygon
The sum of the measures of the angles of a polygon is given by
S = 180 (n – 2)
Where n represents the number of sides.
The sum of the
interior angles
is 540
n = 5
S = 180 (n – 2)
S = 180 (5 – 2) = 180 (3)
S = 540

7. Work this problem Find the sum of the measures
of the interior angles of this
polygon.
This is a hexagon, so it has
6 sides.
S = 180 (n – 2)
What is the measure
of an individual
interior angle?
S = 180 (6 – 2)
S = 180 ( 4)
The measure of an
individual interior angle
is 720/6 = 120
S = 720