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Section 3-5: The Polygon Angle-Sum Theorem

Chapter 3: Parallel and Perpendicular Lines. Section 3-5: The Polygon Angle-Sum Theorem. Objectives. To classify polygons. To find the sums of the measures of the interior and exterior angles of a polygon. Vocabulary. Polygon Convex Polygon Concave Polygon Equilateral Polygon

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Section 3-5: The Polygon Angle-Sum Theorem

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  1. Chapter 3: Parallel and Perpendicular Lines Section 3-5: The Polygon Angle-Sum Theorem

  2. Objectives • To classify polygons. • To find the sums of the measures of the interior and exterior angles of a polygon.

  3. Vocabulary • Polygon • Convex Polygon • Concave Polygon • Equilateral Polygon • Equiangular Polygon • Regular Polygon

  4. Polygon • A polygon is 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.

  5. Are the following figures polygons?

  6. Naming a Polygon

  7. Classification of Polygons by Sides

  8. Convex Polygon • A convex polygon has no diagonal with points outside the polygon.

  9. Concave Polygon • A concave polygon has at least one diagonal with points outside the polygon.

  10. Classify each Polygon • Classify each polygon by its sides. • Identify the polygon as convex or concave.

  11. Theorem 3-14:“Polygon Angle Sum Theorem” • The measures of the angles of an n-gon is:

  12. Finding a Polygon Angle Sum • Find the sum of the measures of the angles of a 15-gon.

  13. Using the Polygon Angle-Sum Theorem • Solve for x.

  14. 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 360º.

  15. Equilateral Polygon • An equilateral polygon has all sides congruent.

  16. Equiangular Polygon • An equiangular polygon has all angles congruent.

  17. Regular Polygon • A regular polygon is both equilateral and equiangular.

  18. Example • Find the measure of an interior angle and an exterior angle of a regular octagon.

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