polygons
DESCRIPTION
Basic properties of polygons, sum of interior anglesTRANSCRIPT
POLYGONS
Triangle eight sides
Heptagon three sides
Octagon seven sides Pentagon four sides
Hexagon five sides
Square six sides
Check your Knowledge: Matching
Triangle six sides
Heptagon three sides
Octagon five sides Pentagon four sides
Hexagon seven sides
Square eight sides
Concave Congruent Convex Corresponding Regular Right
Check your Knowledge: Fill in the Blank
1. A ______________ polygon exists if no line that contains a side of the polygon contains a point in the interior of the polygon.
2. A ______________ polygon is a polygon that is not convex.
3. A ______________ polygon is both equilateral and equiangular.
Concave Congruent Convex Corresponding Regular Right
Check your Knowledge: Fill in the Blank
1. A ______________ polygon exists if no line that contains a side of the polygon contains a point in the interior of the polygon.
2. A ______________ polygon is a polygon that is not convex.
3. A ______________ polygon is both equilateral and equiangular.
Convex
Concave
Regular
vertex
side
vertexB
A
E
D
C
Parts of a Polygon
R
Q
P
S
T
Name the Polygon
Name the Polygon
R
Q
P
S
T
PQRST
Examples: Name the Polygons
D
E
F
K L
J M
A
B
F
D C
E
V
Y
Z
W
X
Sum of the interior angle measures
3 methods for you to choose from
Polygon
n number of sides
number of triangles formed
Sum of the interior angle measures
triangle 3
quadrilateral 4
pentagon 5
hexagon 6
septagon 7
octagon 8
Method 1:
Polygon
n number of sides
number of triangles formed
Sum of the interior angle measures
triangle 3 1
quadrilateral 4 2
pentagon 5 3
hexagon 6 4
septagon 7 5
octagon 8 6
Polygon
n number of sides
number of triangles formed
Sum of the interior angle measures
triangle 3 1 180
quadrilateral 4 2 2 X 180 = 360
pentagon 5 3 3 X 180 = 540
hexagon 6 4 4 X 180 =720
septagon 7 5 5 X 180 =900
octagon 8 6 6x 180 =1080
• The sum of the measures of the angles of an n-gon is
(n-2)180
Method 2:
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 x is 72.
103°, 103°
82
112
132107
x
The measures of three of the interior angles of a quadrilateral are 89°, 110°, and 46°. Find the measure of the fourth interior angle.
82
112
132107
x
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°
107°
Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon,
one at each vertex, is 360.