Transcript Chapter 3 Lesson 4
Chapter 3 Lesson 4 Objective: To classify polygons.
Polygon:
a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear.
B B B A C A C A C E A polygon D E D Not a polygon; not a closed figure D Not a polygon; two sides intersect between endpoints E
Example 1:
Naming a Polygon Name the polygon. Then identify its
vertices
,
sides
, and
angles
.
B
To name a polygon, start at any vertex and list the vertices consecutively in a
A
clockwise or counterclockwise direction.
E
Two names for this polygon are ABCDE CDEAB .
Vertices: A,B,C,D,E and Sides: AB, BC, CD, DE, EA
Angles:
A, B, C, D, E
D C
Example 2:
Three polygons are pictured. Name each polygon, its sides and its angles.
Naming a Polygon
B
Name: ABE Sides: AB, BE, EA
Angles:
A, B, E
A C
Name: BCDE Sides: BC, CD, DE, EB
Angles:
B, C, D, E
E D
Name: ABCDE Sides: AB, BC, CD, DE, EA
Angles:
A, B, C, D, E
You classify a polygon by the number of sides it has.
Sides
3 4 5 6 8 9 10 12
n
Triangle Quadrilateral Pentagon Hexagon Octagon Nonagon Decagon
Name
Dodecagon n-gon
Convex polygon:
polygon.
has no diagonals with points outside the
A B E C Diagonals D
Concave polygon:
the polygon.
has at least one diagonal with points outside
C A B E D F G
Example 3:
Classify each polygon by its sides. Identify each as convex or concave.
a.
b.
Hexagon; Convex Octagon; Concave
Theorem 3-9: Polygon Angle-Sum Theorem
The sum of the measures of the angles of n-gon is (n-2)180.
Example 4:
Find the sum of the measures of the angles of a 15-gon.
For a 15 -gon, n = 15 Sum = ( n – 2)180 ( 15 – 2)180 13•180 2340 Polygon Angle-Sum Theorem Substitute Simplify
Example 5:
Finding a Polygon Angle Sum Find the sum of the measures of the angles of a decagon.
Decagon =
10
( n -2)180 ( 10 -2)180 8•180 1440
Theorem 3-10: Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.
3 2 4 1 5
For the pentagon, m 1 + m 2 + m 3 + m 4 + m 5 = 360.
80° x°
Example 6:
Finding Exterior Angles of a Polygon
150° 80+150+x=360 230+x=360 x=130
Equilateral Polygon:
all sides congruent.
Equiangular Polygon:
all angles congruent.
Regular Polygon:
is both equilateral and equiangular.