The Iranian tile pattern at the right shows several polygons. These polygons can be classified as convex or concave. interior
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1 Page 1 of Classifying Polygons Goal Describe polygons. Key Words convex concave equilateral equiangular regular The Iranian tile pattern at the right shows several polygons. These polygons can be classified as convex or concave. A polygon is convex if no line that contains a side of the polygon passes through the interior of the polygon. A polygon that is not convex is called concave. Convex polygon interior Extended side Concave polygon interior None of the extended sides pass through the interior. At least one extended side passes through the interior. EXAMPLE 1 Identify Convex and Concave Polygons Decide whether the polygon is convex or concave. a. b. Solution a. At least one extended side b. None of the extended sides passes through the interior. pass through the interior. So, the polygon is concave. So, the polygon is convex. 8.1 Classifying Polygons 411
2 Page 2 of 5 A polygon is equilateral if all of its sides are congruent. A polygon is equiangular if all of its interior angles are congruent. A polygon is regular if it is both equilateral and equiangular. Equilateral Equiangular All sides are congruent. All angles are congruent. Regular Polygons All sides are congruent and all angles are congruent. IStudent Help I C L A S S Z O N E. C O M MORE EXAMPLES More examples at classzone.com EXAMPLE 2 Identify Regular Polygons Decide whether the polygon is regular. Explain your answer. a. b. c. Solution a. Although the polygon is equiangular, it is not equilateral. So, the polygon is not regular. b. Because the polygon is both equilateral and equiangular, it is regular. c. Although the polygon is equilateral, it is not equiangular. So, the polygon is not regular. Describe Polygons Decide whether the polygon is convex or concave. Then decide whether the polygon is regular. Explain your answer Chapter 8 Polygons and Area
3 Page 3 of Exercises Guided Practice Vocabulary Check 1. Sketch a concave polygon. 2. Describe the difference between an equilateral polygon and an equiangular polygon. 3. What is a regular polygon? Skill Check Decide whether the polygon shown in black is convex or concave Match the polygon with the description. A. concave B. equilateral C. convex equiangular Practice and Applications Extra Practice See p Convex and Concave Polygons Decide whether the polygon is convex or concave Equilateral and Equiangular Polygons Decide whether the polygon is equilateral, equiangular, or neither. Homework Help Example 1: Exs Example 2: Exs Classifying Polygons 413
4 Page 4 of 5 Regular Polygons Decide whether the polygon is regular. Explain your answer Careers Flooring Decide whether the polygon outlined in red in the floor pattern is convex or concave FLOORING INSTALLERS are hired by flooring contractors to install, repair, or replace floor coverings such as carpet and hardwood. Web site Icons Use the polygons outlined on the website icons shown below. A B C 25. Which polygons are convex? Which polygons are concave? 26. Do any of the polygons appear to be regular? Explain. Student Help LOOK BACK To review the names given to polygons, see p For example, a pentagon has five sides. Logical Reasoning Answer the question about the polygon. 27. Is the triangle 28. Is the parallelogram equiangular? 60 equilateral? Explain. Explain. 60 Visualize It! Decide whether it is possible to sketch a polygon that fits the description. If so, sketch it. 29. A concave pentagon 30. A convex quadrilateral 31. A polygon that is equilateral 32. A polygon that is equiangular but not equiangular but not equilateral 414 Chapter 8 Polygons and Area
5 Page 5 of 5 Finding Perimeters In Exercises 33 35, the polygons are equilateral. Find the perimeter of the polygon in cm ft Using Algebra In Exercises 36 38, the polygons are regular. Find the value of x x x (5x 5) Standardized Test Practice Multiple Choice In Exercises 39 and 40, use the terms below. I. Equilateral II. Equiangular III. Convex IV. Concave 39. Which of the terms best describe the polygon below? A I and III C I and IV B III only D I, II, and III 40. Which of the terms best describe the polygon below? F I and III G I, II, and IV H I and IV J IV only Mixed Review Classifying Polygons Decide whether the figure is a polygon. If so, tell what type. (Lesson 6.1) Algebra Skills Evaluating Powers Evaluate the expression. (Skills Review, p. 668) ( 4) Evaluating Radicals Evaluate. Give the exact value if possible. If not, approximate to the nearest tenth. (Skills Review, p. 668) Classifying Polygons 415
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Form A 1. Find the area of the triangle. 6. A square has a perimeter of 8 inches. Find the area of the square. cm 7. Find the circumference of C in terms of.. Find the area of the parallelogram. 11 cm
Polygons. Discuss with a partner what a POLYGON is. Write down the key qualities a POLYGON has. Share with the class what a polygon is?
Polygons Use a ruler to draw 3 different POLYGONS Discuss with a partner what a POLYGON is Write down the key qualities a POLYGON has Share with the class what a polygon is? *Can you find the area of each