Geometry Section 6.1 Polygons The word polygon means many sides. In simple terms, a polygon is a many-sided closed figure. Formally, a polygon is a figure formed from three or more line segments such that each segment intersects exactly two other segments, one at each endpoint, and no two segments with a common endpoint are collinear. The segments are called the_____ sides of the polygon and the common vertices of endpoints are called the _______ the polygon. When naming a polygon, you must list the vertices in order either clockwise or counterclockwise. The polygon at the right could be named _______ BAFEDC ABCDEF or _______ A diagonal of a polygon is a segment joining two nonadjacent vertices. A polygon is equilateral iff all its sides are congruent. A polygon is equiangular iff all its angles are congruent. A polygon that is both equilateral and equiangular is called a _______ regular polygon. The center of a regular polygon is the point which is equidistant from each of the vertices. A central angle of a polygon is an angle whose vertex is the center and whose sides are radii. A polygon is convex iff the line containing a side does not contain a point in the interior. A polygon that is not convex is concave. Polygons are classified according to the number of its sides. triangle 3 - ____________ 5 - ____________ pentagon 7 - ____________ heptagon nonagon 9 - ____________ dodecagon 12 - ___________ 4 - ____________ quadrilateral hexagon 6 - ____________ octagon 8 - ____________ decagon 10 - ___________ n - ___________ n - gon Example: How many diagonals can be drawn from one vertex in a hexagon? diagonals from 1 vertex # of vertices - 3 Example: How many total diagonals can be drawn in a hexagon? a heptagon? 3 3 2 1 Example: What would you call a regular quadrilateral? square Example: Draw a nonconvex octagon. Example: What is the measure of each central angle in a regular pentagon? dodecagon? 360 360 72 5 12 30