2 PolygonsDefinition:A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints.These figures are not polygonsThese figures are polygons
3 Classifications of a Polygon Convex:No line containing a side of the polygon contains a point in its interiorConcave:A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.
4 Classifications of a Polygon Regular:A convex polygon in which all interior angles have the same measure and all sides are the same lengthIrregular:Two sides (or two interior angles) are not congruent.
5 Polygon Names Classified by the number of sides Triangle4 sidesQuadrilateral5 sidesPentagon6 sidesHexagon7 sidesHeptagon8 sidesOctagon9 sidesNonagon10 sidesDecagonDodecagon12 sidesn sidesn-gon
6 Convex Polygon Formulas….. Diagonals of a Polygon:A segment connecting nonconsecutive vertices of a polygonFor a convex polygon with n sides:The more sides a polygon has, the more diagonals it will have.A square has 2 diagonals.A pentagon has 5 diagonals.A hexagon has 9 diagonals………
7 Examples Diagonals in a square, n = 4 Diagonals in an octagon, n = 8 ** What about a triangle?A triangle does not have ANYdiagonals.Diagonals in an octagon, n = 8
8 Polygon Angle Formulas Finding the INTERIOR angles in a convex polygon with n sides:The sum of the interior angles isThe measure of one interior angle isFinding the EXTERIOR angles in a convex polygon with n sides:The sum of the exterior angles isThe measure of one exterior angle is
9 Solving for the Angles Polygon Triangle Quadrilateral Pentagon Hexagon Interior Angle Sum180360540720Each Interior Angle6090108120Exterior Angle SumEach Exterior Angle72
10 Solving for the Angles Polygon Heptagon Octagon Nonagon Decagon Interior Angle SumEach Interior AngleExterior Angle SumEach Exterior Angle
11 Examples….. Sum of the measures of the interior angles of a 11-gon is The measure of an exterior angle of a regular octagon isThe number of sides of regular polygon with exterior angle 72 ° isThe measure of an interior angle of a regular polygon with 30 sides