# Geometry: Polygons

### Terms and Formulae

#### Terms

Adjacent Sides  -  Sides of a polygon that share a vertex.
Base  -  One of the parallel sides of a trapezoid.
Center of a Regular Polygon  -  The point on the interior of a polygon from which all vertices of the polygon are equidistant.
Closed Curve  -  A curve whose starting point is the same as its ending point.
Concave Polygon  -  A polygon with one or more interior angles greater than 180 degrees.
Congruent Polygons  -  Polygons whose sides are all congruent
Consecutive Vertices  -  Vertices of a polygon that include the endpoints of the same side.
Continuous  -  Without any gaps or holes.
Convex Polygon  -  A polygon whose interior angles are all less than 180 degrees.
Consecutive Angles  -  Angles in a polygon that share a segment as one of the sides that could be extended into a ray.
Curve  -  An arrangement of continuous points in space.
Decagon  -  A ten-sided polygon.
Diagonal  -  A line segment joining nonconsecutive vertices of a polygon.
Dodecagon  -  A twelve-sided polygon.
Equiangular Polygon  -  A polygon whose angles are congruent.
Equilateral Polygon  -  A polygon whose sides are congruent.
Exterior Angle  -  The angle formed at a vertex of a polygon that lies outside of the region enclosed by a polygon.
Heptagon  -  A seven-sided polygon.
Hexagon  -  A six-sided polygon.
Interior Angle  -  The angle formed, at a vertex of a polygon, that lies inside the region enclosed by the polygon.
Leg  -  One of the nonparallel sides of a trapezoid.
Median  -  The segment in a trapezoid whose endpoints are the midpoints of the legs of the trapezoid.
Nonagon  -  A nine-sided polygon.
Opposite sides  -  Sides of a quadrilateral that don't share a vertex.
Octagon  -  An eight-sided polygon.
Parallelogram  -  A quadrilateral with two pairs of parallel sides.
Pentagon  -  A five-sided polygon.
Polygon  -  A simple closed curve consisting of the union of segments that intersect each other at their endpoints.
Rectangle  -  A quadrilateral with four congruent angles.
Regular Polygon  -  An equilateral, equiangular polygon.
Rhombus  -  A quadrilateral with four congruent sides.
Side  -  One segment that comprises part of a polygon.
Simple Closed Curve  -  A closed curve that does not intersect itself.
Square  -  A quadrilateral with four congruent sides and angles.
Trapezoid  -  A quadrilateral with one pair of parallel sides.
Triangle  -  A three-sided polygon.
Vertex  -  The common endpoint of two sides of a polygon.

#### Formulae

 Diagonal Sum A polygon with n sides has n(n-3)/2 diagonals.

 Interior Angle Sum The interior angle sum of a polygon with n sides is 180(n-2) degrees.

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