This document defines and describes various types of polygons including: convex polygons which have no interior angles, concave polygons which have interior angles, equilateral polygons with all sides congruent, equiangular polygons with all interior angles congruent, and regular polygons which are both equilateral and equiangular. It also defines vertices, diagonals, and explains the interior angle sum theorem for quadrilaterals.

1. Terms of Endearment
Polygons: 6.1

2. Polygon
• Plane figure with the following
conditions:
• Formed by 3 or more segments (sides),
such that no two sides with common
endpoints are collinear
• Each side intersects exactly two other
sides, one at each point

3. Vertex of a Polygon
• Each endpoint of a side (the point of
intersection for each side of a
polygon)

4. Convex Polygon
• No line containing a side of the
polygon contains a point on the
interior of the polygon
• Basically, if you were to extend a
side in both directions (forming the
line mentioned above), the extension
of the side would not go through the
inside of the polygon

5. Concave Polygon
• The extension of a side of a polygon
does go through the interior of the
polygon

6. Equilateral Polygon
• A polygon with all of its sides
congruent

7. Equiangular Polygon
• A polygon with all of its interior
angles congruent

8. Regular Polygon
•A polygon is “regular” if it is equilateral
and equiangular

9. Diagonal of a Polygon
•Segment that joins two non-consecutive
vertices
•Basically, a diagonal connects two corners
that don’t connect to form one of the sides
•A rectangle would have two diagonals
(forming an X) on its interior

10. Interior Angles of a Quadrilateral
• This Theorem says that the sum of
the interior angles in a quadrilateral
(4-sided figure) is 360
• To justify this, a rectangle can be
split to form two triangles…each
triangle has a sum of 180 degrees…
so 180 + 180 = 360