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Understanding Polygons and Angle-Sum Theorems in Geometry

This resource covers fundamental concepts related to polygons, including their definitions, types, and the essential Polygon Angle-Sum Theorems. Students will learn how to classify polygons based on the number of sides and understand the relationship between the number of sides and the sum of interior and exterior angles. Engage with various examples, including calculations for angle sums in different polygons, and practice questions to solidify comprehension of these geometric principles.

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Understanding Polygons and Angle-Sum Theorems in Geometry

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  1. Geometry • Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT

  2. Practice

  3. Quiz Time Good Luck!!!

  4. Chapter 3 3-4 The Polygon Angle-Sum Theorems

  5. Polygon • A closed figure that consists of three or more segments joined at the endpoints and each segment must meet exactly two other segments.

  6. Polygon Terms • 3 sides Triangle • 4 sides Quadrilateral • 5 sides Pentagon • 6 sides Hexagon • 7 sides Heptagon • 8 sides Octagon • 9 sides Nonagon • 10 sides Decagon • 11 sides Undecagon • 12 sides Dodecagon • n sides n-gon

  7. Naming A Polygon • A polygon is named by the number of sides. ex: If a polygon has 5 sides, you use 5 letters. Polygon ABCDE

  8. Types of Polygons • Convex • The diagonals are entirely inside the figure. • Concave • At least one diagonal is partly outside the figure.

  9. Regular Polygon • Remember: equilateral, equiangular • A regular polygon is a polygon that is both equilateral and equiangular.

  10. Theorem 3-9Polygon Angle-Sum Theorem • The sum of the measures of the angles of an n-gon is (n-2)180. ex: This pentagon has 5 sides.

  11. Theorem 3-10Polygon Exterior Angle-Sum Theorem • The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360. ex: This pentagon has 5 sides. The sum of the 5 exterior angles is 360.

  12. Example #1 • Name the polygon. Identify vertices, sides, and angles. Is it concave or convex?

  13. Example #2 • Find the interior angle sum. a. 13-gon b. decagon

  14. Example #3 • How many sides does each polygon have if its interior angle sum is: a. 2700 b. 1080

  15. Example #4 • Find x.

  16. Example #5 • Find y.

  17. Example #6 • Find x.

  18. Example #7 • Find x.

  19. Example #8 • Find x.

  20. Example #9 • How many sides does each regular polygon have if its exterior angle is: a. 120 b. 24

  21. Example #10 • How many sides does each regular polygon have if its interior angle is: a. 90 b. 144

  22. Practice • WB 3-4 # 1-19 • EXIT

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