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