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Chapter 3 Lesson 4

Chapter 3 Lesson 4. Objective: To classify polygons. Polygon: a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear. B. B. B. A. A. A. C. C. C. D. E. D. E. D. E.

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Chapter 3 Lesson 4

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  1. Chapter 3 Lesson 4 Objective: To classify polygons.

  2. Polygon: a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides are collinear. B B B A A A C C C D E D E D E Not a polygon; two sides intersect between endpoints Not a polygon; not a closed figure A polygon

  3. B A C E D Example 1:Naming a Polygon Name the polygon. Then identify its vertices, sides, and angles. To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counterclockwise direction. Two names for this polygon are ABCDE and CDEAB. Vertices: A,B,C,D,E Sides: AB, BC, CD, DE, EA Angles: A, B, C, D, E

  4. Name: ABE Sides: AB, BE, EA Angles: A, B, E Name: BCDE Sides: BC, CD, DE, EB Angles: B, C, D, E Name: ABCDE Angles: A, B, C, D, E Sides: AB, BC, CD, CE, EA Example 2:Naming a Polygon Three polygons are pictured. Name each polygon, its sides and its angles. B C A D E

  5. You classify a polygon by the number of sides it has.

  6. Convex polygon:has no diagonals with points outside the polygon. A B C E Diagonals D

  7. Concave polygon:has at least one diagonal with points outside the polygon. C D B E F A G

  8. Example 3: Classify each polygon by its sides. Identify each as convex or concave. a. b. Hexagon; Convex Octagon; Concave

  9. Theorem 3-9:Polygon Angle-Sum Theorem The sum of the measures of the angles of n-gon is (n-2)180. Example 4: Find the sum of the measures of the angles of a 15-gon. For a 15-gon, n = 15 Sum = (n – 2)180 (15 – 2)180 13•180 2340 Polygon Angle-Sum Theorem Substitute Simplify

  10. Example 5:Finding a Polygon Angle Sum Find the sum of the measures of the angles of a decagon. Decagon = 10 (n-2)180 (10-2)180 8•180 1440

  11. 3 2 4 1 5 Theorem 3-10: Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. For the pentagon, m 1 + m 2 + m 3 + m 4 + m 5 = 360.

  12. Example 6:Finding Exterior Angles of a Polygon 80+150+x=360 230+x=360 x=130 80° 150° x°

  13. Equilateral Polygon: all sides congruent. Equiangular Polygon: all angles congruent. Regular Polygon: is both equilateral and equiangular.

  14. Homework Page 147 – 149 #1-25; 32 – 35; 47 - 49

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