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_____ of the polygon and the common endpoints are called the _______ of the polygon. sides vertices

When naming a polygon, you must list the vertices in order either clockwise or counterclockwise. The polygon at the right could be named _______ or _______ ABCDEF BAFEDC

A diagonal of a polygon is a segment joining two nonadjacent vertices.

A polygon is equilateral iff A polygon is equiangular iff A polygon that is both equilateral and equiangular is called a _______ polygon. all its sides are congruent. all its angles are congruent. regular

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. 3 - ____________ 4 - ____________ 5 - ____________ 6 - ____________ 7 - ____________ 8 - ____________ 9 - ____________ 10 - ___________ 12 - ___________ n - ___________ triangle quadrilateral pentagon hexagon heptagon octagon nonagondecagon dodecagon n - gon

Example: How many diagonals can be drawn from one vertex in a hexagon?

Example: How many total diagonals can be drawn in a hexagon? a heptagon?

Example: What would you call a regular quadrilateral?

Example: Draw a nonconvex octagon.

Example: What is the measure of each central angle in a regular pentagon? dodecagon?