Ch. 10.1: Polygons

1
1.5 Polygons
convex and concave
p. 514-521
GSEs
Primary
M(GM)102 Makes and defends conjectures,
constructs geometric arguments, uses geometric
properties, or uses theorems to solve problems
involving angles, lines, polygons, circles, or
right triangle ratios (sine, cosine, tangent)
within mathematics or across disciplines or
contexts (e.g., Pythagorean Theorem, Triangle
Inequality Theorem).
2
Polygon a closed figure with straight sides
http//en.wikipedia.org/wiki/FileAssorted_polygon
s.svg
3
What is a Polygon ?

• Polygons

• Not Polygons

4
Convex polygon if you extend any side of the
polygon, you will not
go through the figure
Concave polygon the opposite is true (it caves
in)
5
Triangle Sum

• The sum of the measures of the interior angles of
  a triangle is 180o.

A
B
C
6
Example 1

• Name Triangle AWE by its angles

A
3x 5
8x 22
4x - 12
W
E
7
A
B
C
H
G
D
F
E
1) Pick any vertex. 2) Make a darker point at
it. 3) Connect that point to every other vertice
in the polygon
Write down how many non-overlapping triangles are
formed.
8
Exterior angle
x
y
Extend any one side of the figure The acute angle
formed is the exterior angle. Its a linear
pair With the inside angle
9
Springboard p. 93
HANDOUT on investigating polygons angles
Convex Polygon Number of Number of
Sum of interior Sum of ext.
sides
s Angles
Angles
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon 9
n-gon n
10

• The formula for finding the sum of the interior
  angles of any convex polygon is

• The sum of all exterior angles of any convex
  polygon is

11
Regular Polygons

• Polygons where each angle and side is congruent

What is an example of a regular 4 sided polygon?
How about a 3 sided polygons?
12
The formula for finding one interior angle in any
regular polygon.
13
Kite ABRN
80
Find the measure of angle N
120
120
14
Solve for x in the Hexagon
110
2x
80
50
115
130
15

• The measure of one of the interior angles
• of a regular polygon is 160. How many
• sides does the regular polygon have?

16
Homework