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Is it too much to ask for a LITTLE PRECIPITATION?! -Evan

Lesson 4: (3.5) The Polygon Angle-Sum Theorems. LT : To classify polygons and to find the measures of the angles of a polygon. Is it too much to ask for a LITTLE PRECIPITATION?! -Evan. Classifying Polygons.

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Is it too much to ask for a LITTLE PRECIPITATION?! -Evan

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  1. Lesson 4: (3.5) The Polygon Angle-Sum Theorems LT: To classify polygons and to find the measures of the angles of a polygon. Is it too much to ask for a LITTLE PRECIPITATION?! -Evan

  2. Classifying Polygons Polygon: Closed plane figure with at least three sides that are segments intersecting only at their endpoints, and no adjacent sides are collinear. B B B C C C A A A E D D D E E Not a polygon Not a polygon Polygon

  3. Classifying Polygons Note: A diagonal of a polygon is a segments that connects two nonconsecutive vertices. Convex Polygon: A polygon with no diagonal with points outside the polygon Concave Polygon: A polygon with at least one diagonal with points outside the polygon. Convex Concave

  4. Classifying Polygons We can classify polygons according to the number of sides it has. Triangle Quadrilateral Pentagon Hexagon Octagon Nonagon Decagon Dodecagon n-gon

  5. Classifying Polygons Classify each polygon by its sides. Identify each as convex or concave.

  6. Classifying Polygons Equiangular Polygon: A polygon with all angles congruent. Equilateral Polygon: A polygon with all sides congruent. Regular Polygon: A polygon that is both equilateral and equiangular.

  7. Naming Polygons D C G H F K J Polygon: Vertices: Sides: Angles:

  8. Super Fun Activity!  Sketch polygons with 4, 5, 6, 7, and 8 sides on chart paper  Divide into triangles by drawing diagonals from one vertex  Multiply the # of Δ’s by 180 to find the polygon angle-sum Theorem 3-14: Polygon Angle-Sum Theorem: The sum of the measures of the angles in an n-gon is (n – 2)180.

  9. Polygon Angle Sums Find the sum of the measures of the angles of a regular dodecagon. Then find the measure of an interior angle. The sum of the angles of a polygon is 720. Find the number of sides the polygon has and classify it.

  10. Polygon Angle Sums Find x in the following polygon. x° 125° 125°

  11. Polygon Angle Sums 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. For a pentagon: 3 2 4 1 5

  12. Polygon Angle Sums If the measure of an exterior angle of a regular polygon is 30, find the number of sides and classify it.

  13. (3.5) The Polygon Angle-Sum Theorems HOMEWORK: (3.5) Pgs. 161-162; #2-26 even, 32, 34, 40,42 TERMS: Polygon, Convex Polygon, Concave Polygon, Equilateral Polygon, Equiangular Polygon, Regular Polygon It took me like three hours to finish the shading on your upper lip. It's probably the best drawing I've ever done. -Napoleon

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