Transcript 3.4 Polygons - Village Christian Schools

3.4
Polygons
(2 cards)
Polygons
Polygon
Not a
Polygon
Not 1
Polygon
Naming Polygons

Name the Polygon

Name the Vertices

Name the Sides

Name the Angles
B
A
C
D
E
Naming Polygons
Name the Polygon
ABCDE or DCBAE
 Name the Vertices
A, B, C, D, E
 Name the Sides
AB, BC, CD, DE, EA
 Name the Angles

B
A
C
A, B, C, D, E
D
E
Classifying Polygons
3
4
5
6
7
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
9 Nonagon
10 Decagon
11 11-gon
12 Dodecagon
n- gon
8
Classifying Polygons
Convex _________
Concave ________
Classifying Polygons
Convex Hexagon
Concave Heptagon
Polygon Angle-Sum Theorem
The sum of the interior angles is:
(n – 2)180
Where n is the number of sides
See Sketchpad
Find the sum of the measure of the
angles of a 13-gon
( 13 – 2 ) 180
(11) 180
1980 degrees
Find the measure of the
missing angle


First find the total
degrees:
(5-2)180
540
Write an equation
100
105
117
117+100+105+115+y=540

Solve
437 + y = 540
y = 103
115
y
Polygon Exterior
Angle-Sum Theorem
The sum of the measures of the
exterior angles of a polygon, one at
each vertex, is
360
1
2
3
6
m1 + m2 + m3 + m4 + m5 + m6 = 360 5
See Sketchpad
4
Definitions


Equilateral Polygon
All Sides congruent
Equiangular Polygon
All Angles congruent
Regular Polygon
All Sides and Angles congruent

The measure of an exterior angle of a
regular polygon is 36 degrees.
Find the measure of an interior angle and
the number of sides of the polygon
The measure of an exterior angle of a
regular polygon is 36 degrees.
Find the measure of an interior angle and
the number of sides of the polygon


Consider the polygon. What do you
notice about the interior and
exterior angles?
1
They are supplementary
2
The measure of an exterior angle of a
regular polygon is 36 degrees.
Find the measure of an interior angle
and the number of sides of the polygon
The sum of an exterior angle and an
interior angle is 180.
36 + y = 180
y = 144
The Interior angle measures 144
degrees
The measure of an exterior angle of a
regular polygon is 36 degrees.
Find the measure of an interior angle
and the number of sides of the polygon






Regular Polygon
All angles are congruent
Total exterior angles is always 360
360 divided by the angle measure
will give the number of sides
360/36 = 10
10 Sides
Homework

3-4 Pg 147