Polygon Properties
What is a Polygon?
A closed plane figure made up of few line segments that are joined together. The sides don't cross each other. Exactly 2 sides meet at every vertex.
Types of Polygons
Regular - all angles are equal and all sides are the same length. Regular polygons are both equiangular and equilateral.
Equiangular - all angles are equal.
Equilateral - all sides are the same length.
Convex - a straight line drawn through a convex polygon crosses at most 2 sides. Every interior angle is less than 180°.
Concave - you could draw at least one straight line through a concave polygon that crosses more than two sides. At least 1 interior angle is more than 180°.
Polygon Formulas
(N = # of sides and S = length from center to a corner)
Area of a regular polygon = (1/2) N sin(360°/N) S2
Sum of the interior angles of a polygon = (N - 2) x 180°
The number of diagonals in a polygon = 1/2 N(N-3)
The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N - 2)
Polygon Parts
Side - one of the line segments that make up the polygon.
Vertex - point where two sides meet. Two or more of these points are called vertices.
Diagonal - a line connecting two vertices that isn't a side.
Interior Angle - Angle formed by two adjacent sides inside the polygon.
Exterior Angle - Angle formed by two adjacent sides outside the polygon.
Special Polygons
Special Quadrilaterals - square, rhombus, parallelogram, rectangle, and the trapezoid.
Special Triangles - right, equilateral, isosceles, scalene, acute, obtuse.
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