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Classify polygons based on their sides and angles.
Objectives
6.1: Properties of Polygons
Vocabulary SketchThings to
Remember
PolygonA closed figure formed by 3 or more segments that intersect
only at their endpoints.
DiagonalA segment that connects
non-consecutive vertices.
Quadrilateral
A four-sided polygon.
Pentagon A five-sided polygon.
Hexagon A six-sided polygon.
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Vocabulary SketchThings to
Remember
Heptagon A seven-sided polygon.
Octagon An eight-sided polygon.
Nonagon A nine-sided polygon.
Decagon A ten-sided polygon.
Dodecagon
A twelve-sided polygon.
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Vocabulary Sketch Things to Remember
n-gon A polygon with n number of sides.
Regular Polygon
An equilateral AND equiangular polygon.
Irregular Polygon
Any polygon that is NOT regular.
Concave Polygon
Any part of the diagonal lies in the exterior of the
polygon.
Convex Polygon
All diagonals lie in the interior of the polygon.
Each segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.
6.1: Properties of Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.
polygon, hexagon
1.
Example 1B: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.
polygon, heptagon
2.
Example 1C: Identifying Polygons
Tell whether the figure is a polygon. If it is a polygon, name it by the number of sides.
not a polygon
3.
Check It Out! Example 1a
Tell whether each figure is a polygon. If it is a polygon, name it by the number of its sides.
not a polygon
4.
Check It Out! Example 1b
Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.
polygon, nonagon
5.
Check It Out! Example 1c
Tell whether the figure is a polygon. If it is a polygon, name it by the number of its sides.
not a polygon
6.
All the sides are congruent in an equilateral polygon. All the angles are congruent in an equiangular polygon. A regular polygon is one that is both equilateral and equiangular. If a polygon is not regular, it is called irregular.
A polygon is concave if any part of a diagonal contains points in the exterior of the polygon. If no diagonal contains points in the exterior, then the polygon is convex. A regular polygon is always convex.
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
irregular, convex
7.
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
irregular, concave
8.
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
regular, convex
9.
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
regular, convex
10.
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
irregular, concave
11.
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