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46-47 Polygons skill 6

46-47 Polygons skill 6. Objectives: To classify Polygons To find the sums of the measures of the interior & exterior s of Polygons. Pg 62-63 Polygons. Polygon:. A closed plane figure. w/ at least 3 sides (segments) The sides only intersect at their endpoints

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46-47 Polygons skill 6

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  1. 46-47Polygonsskill 6 Objectives: To classify Polygons To find the sums of the measures of the interior & exterior s of Polygons.

  2. Pg 62-63 Polygons

  3. Polygon: • A closed plane figure. • w/ at least 3 sides (segments) • The sides only intersect at their endpoints • Name it by starting at a vertex & go around the figure clockwise or counterclockwise listing each vertex you come across.

  4. Which of the following figures are polygons? No yes No

  5. Example 1: Name the 3 polygons Top XSTU S T Bottom WVUX X U Big STUVWX V W

  6. I. Classify Polygons by the number of sides it has. Sides 3 4 5 6 7 8 9 10 12 n Name Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon N-gon Interior  Sum

  7. II. Also classify polygons by their Shape a) Convex Polygon – Has no diagonal w/ points outside the polygon. E A D B C b) Concave Polygon – Has at least one diagonal w/ points outside the polygon. * All polygons are convex unless stated otherwise.

  8. III.Polygon Interior  sum 4 sides 2 Δs 2 • 180 = 360 5 sides 3 Δs 3 • 180 = 540

  9. 6 sides 4 Δs 4 • 180 = 720 • All interior  sums are multiple of 180° Th(3-9) Polygon Angle – Sum Thm S = (n -2) 180 Sum of Interior  # of sides

  10. Find the interior  sum of a 15 – gon. S = (n – 2)180 S = (15 – 2)180 S = (13)180 S = 2340 Find the number of sides of a polygon if it has an  sum of 900°. S = (n – 2)180 900 = (n – 2)180 5 = n – 2 n = 7 sides Examples 2 & 3:

  11. Special Polygons: • Equilateral Polygon – All sides are . • Equiangular Polygon – All s are . • Regular Polygon – Both Equilateral & Equiangular.

  12. IV. Exterior s of a polygon. 1 3 2 1 2 3 4 5

  13. Th(3-10) Polygon Exterior  -Sum Thm • The sum of the measures of the exterior s of a polygon is 360°. • Only one exterior  per vertex. 1 2 3 m1 + m2 + m3 + m4 + m5 = 360 5 4 For Regular Polygons The interior  & the exterior  are Supplementary. = measure of one exterior  Int + Ext = 180

  14. Example 4: • How many sides does a polygon have if it has an exterior  measure of 36°. = 36 360 = 36n 10 = n

  15. Example 5: • Find the sum of the interior s of a polygon if it has one exterior  measure of 24. S = (n - 2)180 = (15 – 2)180 = (13)180 = 2340 = 24 n = 15

  16. Example 6: • Solve for x in the following example. x 4 sides Total sum of interior s = 360 100 90 + 90 + 100 + x = 360 280 + x = 360 x = 80

  17. Example 7: Find the measure of one interior  of a regular hexagon. S = (n – 2)180 = (6 – 2)180 = (4)180 = 720 = 120

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