Classifying Polygons Section 8.1

Objectives Describe polygons.

Key Vocabulary Concave Convex Equilateral polygon Equiangular polygon Regular polygon

Polygons Polygon – a closed figure whose sides are formed by a finite number of coplanar segments called sides. the sides that have a common endpoint are noncollinear each side intersects exactly two other sides, but only at their endpoints. The vertex of each angle is a vertex of the polygon. A polygon is named by using the letters of its vertices, written in consecutive order.

Polygons - Examples

Types of Polygons If the lines of any segment of the polygon are drawn and any of the lines contain points that lie in the interior of the polygon, then it is concave. Otherwise, it is convex (no points of the lines are in the interior).

Classifying Polygons Polygons are classified by the number of sides they have. A polygon with n number of sides is an n-gon. Polygon Number of Sides Triangle 3 Quadrilateral 4 Pentagon 5 Hexagon 6 Heptagon 7 Octagon 8 Nonagon 9 Decagon 10 Hendecagon 11 Dodecagon 12

More Classifying Polygons An equilateral polygon is a polygon in which all sides are congruent. An equiangular polygon is a polygon in which all angles are congruent.

Regular Polygons A convex polygon in which all of the sides and all of the angles are congruent is called a regular polygon. An irregular polygon is a polygon that is not regular. Regular Polygons

Example Regular Polygon? ( ) ( ) ( )) ( (( yes NO! NO!

Decide whether the polygon is convex or concave. Example 1 Identify Convex and Concave Polygons Decide whether the polygon is convex or concave. a. b. SOLUTION a. At least one extended side passes through the interior. So, the polygon is concave. b. None of the extended sides pass through the interior. So, the polygon is convex. 11

Decide whether the polygon is regular. Explain your answer. Example 2 Identify Regular Polygons Decide whether the polygon is regular. Explain your answer. a. b. c. SOLUTION Although the polygon is equiangular, it is not equilateral. So, the polygon is not regular. a. Because the polygon is both equilateral and equiangular, it is regular. b. Although the polygon is equilateral, it is not equiangular. So, the polygon is not regular. c. 12

Your Turn: Decide whether the polygon is convex or concave. Then decide whether the polygon is regular. Explain your answer. ANSWER convex; not regular (equilateral but not equiangular) 1. ANSWER concave; not regular (equilateral but not equiangular) 2. ANSWER convex; regular (both equilateral and equiangular) 3.

Example 3a: Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 4 sides, so this is a quadrilateral. No line containing any of the sides will pass through the interior of the quadrilateral, so it is convex. The sides are not congruent, so it is irregular. Answer: quadrilateral, convex, irregular

Example 3b: Name the polygon by its number of sides. Then classify it as convex or concave, regular or irregular. There are 9 sides, so this is a nonagon. A line containing some of the sides will pass through the interior of the nonagon, so it is concave. The sides are not congruent, so it is irregular. Answer: nonagon, concave, irregular

Your Turn: Name each polygon by the number of sides. Then classify it as convex or concave, regular or irregular. a. b. Answer: triangle, convex, regular Answer: quadrilateral, convex, irregular

Assignment Pg. 413 – 415: #3 – 43 odd