Section 6.1 “Introduction to Polygons”
A polygon is a closed figure in a plane , formed by connecting line segments endpoint to endpoint with each segment intersecting exactly two other segments.
Each line segment is called a side of the polygon. Each endpoint is called a vertex.
Each polygon is classified by the number of sides it has. The polygon names you have to memorize include:
# of sides type of polygon
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 nonagon
10 decagon
11 undecagon
12 dodecagon
n n-gon
When you name a polygon you list the vertices in consecutive order. You can go clockwise or counter-clockwise and you can start at any vertex point.
Example:
How many ways can you name the following polygon?
A diagonal of a polygon is a line segment that connects two nonconsecutive vertices.
How many diagonals are in the following polygon?
A polygon is convex if no diagonal is formed outside of the polygon or if there is no indentation in the figure.
Example of a convex polygon:
Notice how all of the diagonals are located inside the actual polygon.
A polygon is concave if at least one diagonal is formed outside of the polygon or if there are no indentations in the figure.
Notice how the red diagonal is located outside of the polygon. Always look for an indentation within the figure for convex polygons.
Quadrilateral Interior Angles Theorem
The sum of the interior angles of a quadrilateral equals 360 degrees.
Congruent Polygons
Two polygons are congruent if all of the corresponding sides and angles of both polygons have the same length and measure.
Key Terms:
1) An equilateral polygon has sides that are all the same length.
2) An equiangular polygon has
angles that are all have the same
measure.
3) A regular polygon is a polygon that
is both equilateral and equiangular.