Oct 4, 2012 ... Mar 1212:10 PM. Angle Sum of Polygons. Step 1. Draw convex polygons with
three sides, four sides, five sides, and six sides on the.
104 angles of polygons.notebook
October 04, 2012
Convex
Start a new page in your vocab area called "Unit 2 Vocab." Copy all yellow highlighted vocabulary terms for from pages 303, 411, and 412 as well as their definitions.
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Concave
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Equilateral
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Equiangular
Regular Equilateral + Equiangular
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1
104 angles of polygons.notebook
October 04, 2012
Checkpoint 1 3 (pg. 412) Decide whether the polygon is convex or concave. Then decide if the polygon is regular. Explain your answer.
1.
2.
3.
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How do we name polygons?
POLYGONS
A
vertex
B
E
side
C
D
What makes a polygon a polygon? 1. Formed by three or more segments. 2. Each segment intersects with exactly two other segments at each of its endpoints.
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What is a diagonal of a polygon?
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POLYGONS?
A B
A
B
C
D
E
D
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C
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2
104 angles of polygons.notebook
October 04, 2012
CLASSIFY THE POLYGON
Types of polygons Number of sides
Classification of polygon
A
E
1.
D
H
F
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Checkpoint 1 4 (pg. 304)
C
B
G
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Decide whether the figure is a polygon. If so, tell what type. If not, explain why.
6
5
4
3
2. Number of sides
Polygon
Number of triangles
Sum of measures of interior angles
Triangle Quadrilateral
Pentagon
3.
4.
Hexagon
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Angle Sum of Polygons Step 1 Draw convex polygons with three sides, four sides, five sides, and six sides on the back of this paper. Step 2 Draw all possible diagonals from a single vertex within each polygon. Step 3 Complete the table based on the data from your diagrams. Polygon
Number of sides
Number of triangles
Sum of measures of interior angles
Triangle
3
1
1 180o = 180o
Polygon Interior Angles Theorem The sum of the measures of the interior angles of a convex polygon with n sides is (n 2) 180o
n = number of sides
Quadrilateral
Pentagon Hexagon Extension 1. Look for a pattern in the last column of the table. What is the sum of the measures of the interior angles of a heptagon? Of an octagon? heptagon _____________ octagon ______________
2. Write an expression for the sum of the measures of the interior angles of any convex polygon with n sides. ______________ (Hint: Look at the number of triangles compared with the number of sides of each polygon.)
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Mar 1211:36 AM
3
104 angles of polygons.notebook
EXAMPLE
Find the sum of the measures of the interior angles of a convex heptagon.
October 04, 2012
EXAMPLE Find the measure m A.
D
142o
88o
C 136
E 105o
o
F
136o
B
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EXAMPLE
Find the measure of an interior angle of the regular octagon.
A
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Checkpoint 1 3 (pg. 418) In exercises 13, find the measure of G.
1.
F 111o
G
H
2.
103o o 133
J
E 118o
3.
109o 130o H D H J 140o 140o G
G
K
4. K
o F 120
L
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150o
58o
Find the measure of an interior angle of a regular polygon with twelve sides.
