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Warm Up
1. How many sides do the following figures have?
a) b)
2. Solve for x.
352x + 7
50 2x - 12
a) b)
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Section 1.6
Classifying Polygons
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A Polygon is a closed plane figure with the following properties:
What is a Polygon?
1) Is formed by 3 or more line segments (sides)
2) Each side intersects exactly 2 sides, but only at their endpoints
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If a polygon is convex then no sides go through the interior of the polygon.
(All vertices point outside the polygon.)
If a polygon is concave then it is not convex. A side goes through the interior of the polygon.
(At least one vertex points inside the polygon.)
A Polygon can either be convex or concave.
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A Polygon can either be convex or concave.
convex
• no sides go through the interior of the polygon.
• A side goes through the interior of the polygon.
concave
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Example 1:Which figures are polygons?
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Example 1:Which figures are polygons?
polygon polygon polygon
polygon
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Example 2:
Label the polygons as convex or concave?
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Example 2:
Label the polygons as convex or concave?
convex concave concave convex
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Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.
Vertices Interior Angles Exterior Angles
Perimeter AreaSides
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Parts of a polygon
Vertices – each endpoint of a side
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Parts of a polygon
Interior Angles
)
)
)
)
)
)
)
)
))
)
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Parts of a polygon
Exterior Angles
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Parts of a polygon
Sides
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Parts of a polygon
Perimeter
Add all sides
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Parts of a polygon
Area
Amount of surface covered by a figure
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Parts of a polygonIn more complex polygons there are more parts.Learn these new terms:
Diagonal RegularConsecutive
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Parts of a polygon
Refers to parts that are right next to each other.
(They share a common vertex or side.)
Consecutive (side/angles))
)
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Parts of a polygon
Diagonal
A segment that joins two nonconsecutive vertices.(Notice the triangle does NOT have any diagonals.)
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Parts of a polygon
A convex polygon that is equilateral and equiangular.)
)
)
)
)
))
))
)
)Regular
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A Polygon is classified by its’ number of sides.
3
4
5
6
7
8
9
10
12
n n - gonDodecagon
Decagon
Nonagon
Octagon
Heptagon
Hexagon
Pentagon
Quadrilateral
Triangle
Number of Sides Type of Polygon
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A Polygon is classified by its’ number of sides.
ex: 100-gon -refers to a polygon with 100 sides
• n-gon : can be used to name a polygon n = number of side
3 4 5
10
78 9
6
11
What do you notice as n gets bigger?
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ExamplesName each polygon by its number of sides. Then classify it as convex or concave and equilateral, equiangular, or regular.
4
4 4
4
)
)
))
)
)
))
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Tell Whether the statement is always, sometimes, or never true.
Examples
A regular polygon is equiangular.
A triangle is convex.
A regular polygon is equilateral.
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Example
The expression (-2x + 41) and (7x - 40) represent the lengths of two sides of a equilateral pentagon. Find the side of the pentagon.
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Example
The expression (9x + 5) and (11x - 25) represent the measures of two angles of a regular nonagon. Find the measure of angle of the nonagon.
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Homework
Workbook p16#’s 1-23 odd