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Geometry
Unit V
Section 6.1: Polygons
The word polygon means __many sides___. In simple terms, a polygon is a ___many-sided figure_____.
Formally, a polygon is a figure formed from three or more line segments such that
A
each segment intersects exactly two other segments, one at each endpoint, and no
two segments with a common endpoint are collinear. The segments are called the
B
C
F
_sides__ of the polygon and the common endpoints are called the ____vertices____
of the polygon. When naming a polygon, you must __LIST THE VERTICES IN ORDER
CLOCKWISE OR COUNTERCLOCKWISE!!!
The polygon at the right could be named __ABCDEF___ or ___EDCBAF___ or……...
E
D
Diagonal
d
A diagonal of a polygon is ___a segment joining two nonadjacent vertices______.
A polygon is equilateral iff __all its sides are equal__________.
A polygon is equiangular iff __all its angles are equal_______________.
A polygon that is both equilateral and equiangular is called a ____regular______ polygon.
The center of a regular polygon is the point which ___is equidistant from each of the vertices______.
The central angles of a polygon is _____the angles that have the center as vertex__.
A polygon is convex iff _____the line containing a side does not contain a point in the interior________
A polygon that is not convex is ___concave________.
Polygons are classified according to the number of its sides.
quadrilateral
triangle
3 - ____________________
4 - ____________________
hexagon
6 - ____________________
7 - ____________________
nonagon
9 - ____________________
n-gon
n - ____________________
pentagon
5 - ____________________
octagon
heptagon
8 - ____________________
decagon
12 - ____________________
10 - ____________________
dodecagon
Example: How many diagonals can be drawn from one vertex in a hexagon? Decagon?
three
seven
What do all the diagonals from one vertex do to the polygon?
Split it into triangles
(N-2)
triangles
How many? ______________________
Equation to find the total number of diagonals:
𝑛(𝑛 − 3)
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑎𝑔𝑜𝑛𝑎𝑙𝑠 =
2
9
Example: What would you call a regular quadrilateral?
square
Example: Draw a nonconvex octagon.
Example: What is the measure of each central angle in a regular pentagon? dodecagon?
y
5 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒𝑠
360
= 72 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
5
12 𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒𝑠
360
= 30 𝑑𝑒𝑔𝑟𝑒𝑒𝑠
12