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# The Polygon Angle-Sum Theorems

The Polygon Angle-Sum Theorems. Aimee Brewer 3 rd period Lesson 3-5. Vocabulary. Polygon: a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides. octagon. hexagon. triangle. Non polygons. B. C. H. I. A.

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## The Polygon Angle-Sum Theorems

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1. The Polygon Angle-Sum Theorems Aimee Brewer 3rd period Lesson 3-5

2. Vocabulary Polygon: a closed plane figure with at least three sides that are segments. The sides intersect only at their endpoints, and no adjacent sides. octagon hexagon triangle

3. Non polygons B C H I A D J F E K Not a closed figure L 2 sides intersect between endpoints

4. Vocabulary Convex Polygon: has no diagonal with points outside the polygon. Concave Polygon: has at least one diagonal with points outside the polygon.

5. Vocabulary Equilateral Polygon: has all sides congruent. Equiangular Polygon: has all angles congruent. Regular Polygon: is both equilateral and equiangular.

6. Naming Polygons To name a polygon, start at any vertex and list the vertices consecutively in a clockwise or counterclockwise direction.

7. Examples E W X Z Y F G Polygon WXYZ Polygon EFG

8. To name sides and angles S I H J K V U Sides: SU, SV, VU Angles: <S, <U, <V Sides: HI, IJ, JK, KH Angles: <H, <I,<J, <K

9. Theorem 3-14 Polygon Angle-Sum Theorem: The sum of the measures of the angles of an n-gon is (n-2)180

10. Example Finding the sum of a 12-gon (N-2) 180 N=12 (12-2) 180 (10) 180 N= 1800

11. Theorem 3-15 Polygon Exterior Angle-Sum Theorem: The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. <1+<2+<3+<4+<5=360 1 2 5 3 4

12. Quiz • Is this a polygon? • Find the sum of a 20-gon • Name are the sides and angles P R Q

13. Answers • No • 3240 • sides: PQ, QR, RP; Angles: <R,<P,<Q

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