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# Polygons

## on Mar 01, 2011

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Basic properties of polygons, sum of interior angles

Basic properties of polygons, sum of interior angles

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## PolygonsPresentation Transcript

• Polygons
Triangle eight sides
Heptagon three sides
Octagon seven sides
Pentagon four sides
Hexagon five sides
Square six sides
• Triangle six sides
Heptagon three sides
Octagon five sides
Pentagon four sides
Hexagon seven sides
Square eight sides
• Check your Knowledge: Fill in the Blank
Concave Congruent Convex
Corresponding Regular Right
A ______________ polygon exists if no line that contains a side of the polygon contains a point in the interior of the polygon.
A ______________ polygon is a polygon that is not convex.
A ______________ polygon is both equilateral and equiangular.
• Check your Knowledge: Fill in the Blank
Concave Congruent Convex
Corresponding Regular Right
Convex
A ______________ polygon exists if no line that contains a side of the polygon contains a point in the interior of the polygon.
A ______________ polygon is a polygon that is not convex.
A ______________ polygon is both equilateral and equiangular.
Concave
Regular
• Parts of a Polygon
• Name the Polygon
S
R
Q
T
P
• Name the Polygon
S
R
PQRST
Q
T
P
• Examples: Name the Polygons
J
M
E
L
K
F
D
V
Z
A
F
B
E
W
Y
X
D
C
• Sum of the interior angle measures
3 methods for you to choose from
• Method 1:
• Method 2:
The sum of the measures of the angles of an n-gon is
(n-2)180
• Method 3:
You know that the sum of the interior angles of every triangle is 180 –
For each side you add to a triangle to make the shape you need, you add 180.
• Find the measure of an interior angle and an exterior angle for the indicated regular polygon
Regular 18-gon
• Find the measure of an interior angle and an exterior angle for the indicated regular polygon
Regular 18-gon
Interior Angles
(n-2)*180 = 2880
2880/18 = 160
• The value of xis 72.
103°, 103°
• 107
132
82
x
112
The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle.
• 107
132
82
x
112
107°
The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle.
115°
• Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon,
one at each vertex,
is 360.