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Learning intentions: What is a polygon? Sum of interior angles in polygons .

Polygon. Learning intentions: What is a polygon? Sum of interior angles in polygons . How can I find angle measures in polygons without using a protractor?. Polygon. Polygon comes from Greek. . Poly- means "many" . gon means "angle". . Many angles. What is a polygon?

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Learning intentions: What is a polygon? Sum of interior angles in polygons .

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  1. Polygon Learning intentions: What is a polygon? Sum of interior angles in polygons.

  2. How can I find angle measures in polygons without using a protractor?

  3. Polygon Polygon comes from Greek. Poly- means "many" gon means "angle". Many angles

  4. What is a polygon? A polygon is a Plane shape with straight sides. Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up). Resource: http://www.mathsisfun.com/geometry/polygons.html

  5. Polygons

  6. Nonexamples

  7. http://www.mathsisfun.com/geometry/polygons.html Types of Polygons Regular or Irregular If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular Concave or Convex A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°. If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it) Convex Concave

  8. Polygons • Can be concave or convex. Concave Convex The diagonals of the convex polygonall lie within the figure. Non-convex polygons have some diagonals that do not lie within the figure. Some interior angles are reflex (greater than 180°).

  9. Polygons are named by number of sides Triangle 3 4 Quadrilateral Pentagon 5 Hexagon 6 Heptagon 7 8 Octagon 9 Nonagon 10 Decagon 12 Dodecagon n n-gon

  10. Sums of Interior Angles

  11. Draw a:  Quadrilateral  Pentagon  Hexagon  Heptagon  Octogon • Then draw diagonals to create triangles. • A diagonal is a segment connecting two nonadjacent vertices (don’t let segments cross) • Add up the angles in all of the triangles in the figure to determine the sum of the angles in the polygon. • Complete this table

  12. Sums of Interior Angles Triangle Quadrilateral Pentagon = 2 triangles = 3 triangles Hexagon Octagon Heptagon = 4 triangles = 5 triangles = 6 triangles

  13. 3 1 180° 4 2 2 x 180 = 360° 5 3 3 x 180 = 540° 4 4 x 180 = 720° 6 7 5 5 x 180 = 900° 8 6 6 x 180 = 1080° n n - 2 (n – 2) x 180°

  14. 3 1 180° 4 2 2 x 180 = 360° 5 3 3 x 180 = 540° 4 4 x 180 = 720° 6 7 5 5 x 180 = 900° 8 6 6 x 180 = 1080° n n - 2 (n – 2) x 180°

  15. The angle sum of a polygon with n sides is given by: angle sum = (n − 2) × 180° or 180(n − 2)° Find the angle sum of a polygon with 18 sides. Solution Angle sum = (18 − 2) × 180° = 16 × 180° = 2880° Find the angle sum of a polygon with sides. Solution Angle sum = (4− 2) × 180° = 2× 180° = 360°.

  16. End

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