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

A polygon is a Plane shape with straight sides. 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

Polygons

Nonexamples

Types of Polygons http://www.mathsisfun.com/geometry/polygons.html 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

Polygons Can be concave or convex. Concave Convex The diagonals of the convex polygon all 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°).

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

Sums of Interior Angles

Then draw diagonals to create triangles. 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 Polygon # of sides # of triangles Sum of interior angles

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

Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon Polygon # of sides # of triangles Sum of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon 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°

Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon Polygon # of sides # of triangles Sum of interior angles Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon n-gon 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°

Find the angle sum of a polygon with 18 sides. Solution 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°.

End