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  • 1. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 Chapter 4.7 Polygons and Angle Measure Polygons are named for the number of sides they have. 3 sides = triangle 8 sides = octagon 4 sides = quadrilateral 9 sides = nonagon 5 sides = pentagon 10 sides = decagon 6 sides = hexagon n sides = n-gon 7 sides = heptagon
  • 2. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 Vocab Vertex ­ intersection of    two sides VERTEX Diagonal ­ segment between       two non­consecutive DIAGONAL       vertices Key Vocab REGULAR A polygon is regular if it is equilateral AND equiangular Name the following shapes by the number of sides. Are these shapes regular? Example: What is the perimeter of a regular nonagon with a side length of 5 cm?
  • 3. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 CONVEX vs. CONCAVE Convex ­ the diagonals are INSIDE the polygon Concave ­ part of the diagonals are OUTSIDE of the polygon By drawing in all of the diagonals from a vertex in a convex polygon, we can cut the shape into triangles
  • 4. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 How many diagonals can be drawn from a vertex in a convex polygon? # of sides # of Diagonals # of Triangles How many DIAGONALS can be drawn in an n­sided polygon? How many TRIANGLES are in an n­sided polygon? If a polygon has n sides, we can draw n­2 triangles inside of it. 5 sides 3 triangles If each of these triangles has  180 degrees.
  • 5. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 IMPORTANTE If a convex polygon has n sides, then the sum of interior angles is: (n ­ 2) 180 Example: (n ­ 2) 180 Find the sum of interior angles for the following convex polygons Hexagon Heptagon Octagon Pentagon Decagon Example What is the measure of ONE interior angle of a regular pentagon? Sum of interior angles (5 ­ 2)  180 3  180 5400 The measure of ONE angle is: 540 ÷ 5 = 1080 Example: What is the measure of ONE interior angle of a regular hexagon?
  • 6. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 The sum of exterior angles for ANY convex polygon is ALWAYS 3600 t x t + x + y + z + w = 360 w y z Example: Find the sum of exterior angles for the following convex polygons Hexagon Heptagon Octagon Pentagon Decagon Example: What is the measure of ONE exterior angle of a regular heptagon?
  • 7. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 Solve for x 2x 1050 750 x 350 Solve for n n0 1130 370 n0
  • 8. Ch4.7_PolygonsAndAngles.notebook October 31, 2011 Formula Recap Sum of Interior <s Measure of ONE Interior < (n­2) x 180 (n­2) x 180 n Sum of Exterior <s Measure of ONE Exterior < 3600 3600 n Page 180: #6­15, 19­21