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Geometry

Geometry. Agenda 1. ENTRANCE 2. Go over Practice 3. Quiz 4. 3-4 The Polygon Angle-Sum Theorems 5. Practice Assignment 6. EXIT. Practice. Quiz Time Good Luck!!!. Chapter 3. 3-4 The Polygon Angle-Sum Theorems. Polygon.

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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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