Objective: To identify Polygons and the properties of polygons. Use the properties of a polygons to solve

problems. College Geometry

Singleton

polygon

Diagonal

Equilateral

Any shape that has vertices and segments for sides. The sum of the angles is dependant on the number of triangles formed by the diagonals. (n -2)*180

A Segment that connects two nonadjacent vertices.

Equi – equal Lateral – Side When all sides of the polygon have the same length

Equiangular

Regular

Concave

Convex

Equi – equal Angular– Angle When all angles of the polygon have the same degree

Any shape that is both Equilateral and Equiangular.

(n – 2)*180/n for one interior angle

Vertices on the interior of the shape (a caved in appearance)

All vertices on the exterior

Exterior angle An angle formed by extending the side of a shape to form an angle on the exterior. It is a linear pair(supplementary) to the interior angle.

108 x

DecagonPentagon

Heptagon

DodecagonOctagonHexagon

57

6 8

10

12

N – 2 is how we find out how many triangles the diagonals will make

180 is how many degrees a triangle must sum to

(n - 2)*180 will tell us the sum of the angles of any polygon

1

23

4

56

7

8

1

2

3

1

234

(5 – 2) = 3 3 * 180 = 540

(6 – 2) = 4 4 * 180 = 720

(10 – 2) = 8 8 * 180 = 1440

#2 A regular polygon has 8 sides.

i) What is it’s nameii) What is the

measure of each interior angle?

iii) What is the measure of each exterior angle?

62º64º

xº

#1. Solve for x