Transcript Document 7188235

Section 2.5 Convex Polygons
• A polygon is a closed plane figure whose sides are line
segments that intersect only at the endpoints.
• Convex polygons angles are between 0 and 180
• Concave polygons have one angle that is more than
180 (reflex angle) Fig. 2.29 p. 99
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Types of Polygons
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Polygon
Number of
Sides
Triangle
Quadrilateral
Pentagon
3
4
5
Hexagon
Heptagon
Octagon
6
7
8
Nonagon
Decagon
9
10
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Diagonals of a Polygon
• Definition: a line segment
that joins two
nonconsecutive vertices.
• Theorem 2.5.1: The total
number of diagonals D in
a polygon of n sides is
given by the formula:
n( n  3)
D
2
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Polygon
Triangle
Quadrilateral
Number of
Diagonals
0
2
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
5
9
? 14
? 20
? 27
? 35
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Sum of the Interior Angles of a Polygon
Polygon
• Theorem 2.5.2: The sum
S of the measures of the
interior angles of a
polygon with n sides is
given by
S = (n-2) 180
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Triangle
Quadrilateral
Pentagon
Sum of
Interior
Angles
180
360
540
Hexagon
Heptagon
Octagon
720
900 
1080 
Nonagon
Decagon
1260 
1440 
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Regular Polygons
• A polygon that is both equilateral and equiangular
• Corollary 2.5.3: The measure l of each interior angle of a regular
polygon or equiangular polygon of n sides is:
(n  2)  180
l
n
• Corollary 2.5.4: The sum of the four interior angles of a quadrilateral
is 360.
• Corollary 2.5.5: The sum of the measures of the exterior angles of a
polygon, one at each vertex, is 360. Proof p. 104
• Corollary 2.5.6: The measure E of each exterior angle of a regular
polygon or equiangular polygon in n sides is E = 360/n
Ex. 6 p. 104
Polygrams: Figure created when sides of a convex polygon are
extended. Fig. 2.37 p. 109
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