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Page 1 of 5 Polygons Word Watch quadrilateral, p. 494 trapezoid, p. 494 parallelogram, p. 494 rhombus, p. 494 polygon, p. 495 pentagon, p. 495 hexagon, p. 495 heptagon, p. 495 octagon, p. 495 regular polygon, p. 496 BEFORE Now WHY? You classified triangles. You’ll classify quadrilaterals and other polygons. So you can classify the polygons in a stained glass window, as in Ex. 15. A quadrilateral is a geometric figure that is made up of four line segments, called sides, that intersect only at their endpoints. Some quadrilaterals have special names. Special Quadrilaterals Diagram Trapezoid A trapezoid is a quadrilateral with exactly 1 pair of parallel sides. Parallelogram A parallelogram is a quadrilateral with 2 pairs of parallel sides. Rectangle A rectangle is a parallelogram with 4 right angles. Rhombus A rhombus is a parallelogram with 4 congruent sides. Square A square is a parallelogram with 4 right angles and 4 congruent sides. EXAMPLE with Notetaking To help you classify quadrilaterals, you could draw a diagram that shows how the special quadrilaterals are related to each other. 1 Classifying a Quadrilateral Sketch and classify a quadrilateral with opposite sides parallel, one side of length 3 cm, and another side of length 1 cm. 3 cm 1 Draw two sides, one of length 3 cm 1 cm and one of length 1 cm. The angle between the two sides does not matter. 2 Draw sides parallel to the first two sides to complete the figure. ANSWER The figure is a parallelogram. 494 Chapter 10 Geometric Figures 3 cm 1 cm 1 cm 3 cm Page 2 of 5 Your turn now Sketch and classify the quadrilateral described. 1. A quadrilateral with 4 right angles, 4 congruent sides of length 2.5 centimeters, and both pairs of opposite sides parallel Polygons A polygon is a geometric figure that is made up of three or more line segments that intersect only at their endpoints. The number of sides determines the name of the polygon. Classifying Polygons with Reading The prefixes used in the names of polygons tell you the number of sides the figure has. Prefix triquadpentahexaheptaocta- Meaning three four five six seven eight EXAMPLE Triangle Quadrilateral Pentagon 3 sides 4 sides 5 sides Hexagon Heptagon Octagon 6 sides 7 sides 8 sides 2 Classifying Polygons Tell whether the figure is a polygon. If it is, classify it. If it is not, explain why not. a. b. Solution a. This figure is a polygon with 5 sides. So, it is a pentagon. b. This figure is not a polygon because it is not made up entirely of line segments. Your turn now Tell whether the figure is a polygon. If it is, classify it. If it is not, explain why not. 2. 3. 4. Lesson 10.4 Polygons 495 Page 3 of 5 Regular Polygons A regular polygon is a polygon with all sides equal in length and all angles equal in measure. The pentagon shown is an example of a regular polygon. tch Out! Wa Just because a polygon has sides that are all congruent does not necessarily mean that it is a regular polygon. All angles must also be congruent. EXAMPLE 3 Using a Regular Polygon The polygon shown is a regular pentagon. Find the perimeter of the pentagon. Then find the sum of the angle measures in the pentagon. 1 A regular pentagon has 5 sides of equal length, so the perimeter of the pentagon is 5(3) 15 feet. 3 ft 2 A pentagon can be divided into three triangles. The sum of the angle measures in a triangle is 180, so the sum of the angle measures in any pentagon is 180 180 180 540. INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 714 Getting Ready to Practice 1. Vocabulary Copy and complete: Two types of quadrilaterals that have four right angles are _?_ and _?_. Tell whether the figure is a polygon. If it is a polygon, classify it. If it is not, explain why not. 2. 3. 4. 5. Guided Problem Solving The quilt design shown repeatedly uses regular hexagons and other polygons. What is the sum of the angle measures in a hexagon? 1 Sketch a hexagon on a piece of paper. 2 Draw three line segments to divide the hexagon into triangles. 3 Use the triangles to find the sum of the angle measures in a hexagon. 496 Chapter 10 Geometric Figures Page 4 of 5 Practice and Problem Solving with Example 1 2 3 Homework Use the clues to sketch and classify the quadrilateral described. Exercises 6–8 9–16 21–22 6. This figure has four right angles. Not all of the sides are the same Online Resources 8. This figure has exactly one pair of opposite sides that are parallel. CLASSZONE.COM • More Examples • eTutorial Plus length. 7. This figure’s opposite sides are parallel and congruent. Not all of the angles are congruent. Classify the polygon and tell if it is regular. If it is not regular, explain why not. 9. 10. 11. 12. 13. 14. 15. Stained Glass Window Sketch and classify four different polygons contained in the stained glass window. Do any of the polygons appear to be regular? Explain your reasoning. 16. Geometry Graph and connect the ordered pairs (0, 5), (3, 2), (2, 2), (2, 1), (3, 2), and (0, 5) in the order they are given. Is the figure that results a polygon? If it is, classify it and tell if it is regular. If it is not a polygon, explain why not. Critical Thinking Tell whether the statement is true or false. Explain your reasoning. 17. All squares are rectangles. 18. A scalene triangle is regular. 19. A trapezoid is a parallelogram. 20. Every rhombus is a square. Find the measure of each side of the polygon described. 21. A regular octagon with a perimeter of 46 centimeters 22. A regular heptagon with a perimeter of 52.5 inches Lesson 10.4 Polygons 497 Page 5 of 5 Extended Problem Solving In Exercises 23–26, you will examine the angle measures of polygons. 23. Break into Parts Copy and complete the table below. Use the problem solving strategy of breaking into parts. Polygon Triangle Quadrilateral Pentagon Hexagon Sum of angle measures ? ? ? ? Measure of each angle in a regular polygon ? ? ? ? 24. Look for a Pattern What pattern do you notice in the sum of the angle measures in the table? 25. Predict Use the pattern you identified to predict the sum of the angle measures in a heptagon. What do you predict is the measure of each angle in a regular heptagon? 26. Challenge Write an expression for the sum of the angle measures in a regular polygon with n sides. Then write an expression for the measure of each angle in a regular polygon with n sides. 27. Critical Thinking Name a quadrilateral that is always a regular polygon. Explain your reasoning. Mixed Review 28. Your average monthly checking account balance was $580 in January and $957 in March. What was the percent of increase in your account balance from January to March? (Lesson 9.6) 29. Classify a triangle that has angle measures of 25, 105, and 50. (Lesson 10.3) Basic Skills Evaluate the power. 30. 23 31. 3 2 32. 18 33. 54 Test-Taking Practice INTERNET State Test Practice 34. Multiple Choice What is the sum of the angle measures in a parallelogram? CLASSZONE.COM A. 360 B. 270 C. 180 D. 90 35. Multiple Choice What is the perimeter of a regular octagon with a side length of 4 centimeters? F. 12 cm 498 Chapter 10 Geometric Figures G. 16 cm H. 32 cm I. 64 cm