6-1 Properties and Attributes of Polygons
Side of a polygon—Each segment which forms a polygon
Vertex of the polygon—the common endpoint of two sides of a polygon
Diagonal—A segment that connects two nonconsecutive vertices
AB , BC , CD , and DAare sides of the polygon.
AC and BD are diagonals
A, B, C, and D are vertices.
AB , BC , CD , and DAare sides of the polygon.
AC and BD are diagonals
Polygon—a closed plane figure formed by three or more line segments that intersect only at
their endpoints. No two sides with a common endpoint are collinear.
Classifying Polygons.
1. By the length of its sides, measure of its angles, or both
Equilateral Polygon—A polygon which has all sides congruent.
A rhombus is an equilateral
polygon.
Equiangular Polygon- A polygon which has all angles congruent. A rectangle is an
equiangular polygon.
Regular Polygon—a polygon which has all angles and sides congruent.
http://www.google.com/imgres?q=equilateral+polygon+that+is+not+equiangular
2. By convex or concave
Convex—no diagonal contains points in the exterior of the polygon. A
regular polygon is always convex.
Concave—any part of a diagonal contains points in the exterior of the
polygon.
3. By the number of sides it has.
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
Nonagon
Decagon
n-gon
Number of sides
3 sides
4 sides
5 sides
6 sides
7 sides
8 sides
9 sides
10 sides
n sides
To find the sum of the interior angle measures of a convex polygon, draw all
possible diagonals from ONE vertex of the polygon. This gives you a set of
triangles. The sum of the angle measures of all triangles equals the sum of the
angle measures of the polygon. (Remember, the sum of the angles of a triangle
is 180 °.
Polygon Angle Sum Theorem-The sum of the interior angle measures of a convex
polygon with n sides is (n-2) * 180 °.
Polygon
# of sides
# of triangles
Triangle
Quadrilateral
Pentagon
Hexagon
n-gon
3
4
5
6
n
1
2
3
4
n-2
Sum of interior
angle measures
180 °
360 °
540 °
720 °
(n-2) * 180 °
Exterior angle—formed by one side of a polygon and the extension of a
consecutive side. Angle 4 is an exterior angle.
Polygon Exterior Angle Sum Theorem –The sum of the exterior angle measures,
one angle at each vertex, of any convex polygon is 360 °.
http://www.google.com/imgres?q=exterior+angle+sum+theorem&start=192&