1. Other polygons November 12, 2009

2. Objectives Content Objectives Learn about properties of polygons, beyond triangles and quadrilaterals. Language Objectives Students will be able to describe and apply the properties of different polygons.

3. What is a polygon? A polygon is a plane figure formed by a finite number of segments such that (1) sides that have a common endpoint are noncollinear and (2) each side intersects exactly two other sides, but only at their endpoints. A convex polygon is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. Convex polygons with all sides congruent and all angles congruent are called regular.

4. Regular polygons

5. Concave vs. convex A concave polygon is defined as a polygon with one or more interior angles greater than 180°. It looks sort of like a vertex has been 'pushed in' towards the inside of the polygon.

6. Interior Angle Sum Theorem If a convex polygon has n sides and S is the sum of the measures of its interior angles, then: S=180(n-2)

7. Exterior Angle Theorem If a polygon is convex, then the sum of the measures of the exterior angles, one at each vertex, is 360.

8. Naming polygons NameSidesAngles Diagonals Sum of Interior Angles Triangle33 0 Quadrilateral44 2 Pentagon55 5 Hexagon66 9 Heptagon77 14 Octagon88 20 Nonagon99 27 Decagon10 35

9. Exterior and Interior Angles