Post on 17-Dec-2015
Happy Wednesd
ay!!
11.1-Polygon Basicspolygon
“poly” = many…and “gon” = sides
So a polygon is a closed shape with 3 or more sides.
Examples:
Triangle Rectangle Hexagon
11.1-Polygon BasicsEvery polygon has the
same features: Sides – at least 3 sides made of straight line segments
Vertices (aka endpoints) – connects the sides and forms <s
Angles – at least 3 <s with varying degrees (each less than 180°)
11.1-Polygon Basics# of Sides Type of Polygon Pic of Polygon
3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
9 Nonagon
10 Decagon
12 Dodecagon
n n-gon
11.1-Polygon BasicsSpecial Terms for Polygons:
Convex – no line of a side contains a point inside the polygon
Concave (aka nonconvex) – line of a side contains a point inside the polygon
Regular Polygon – convex polygon that is both equilateral and equiangular
Consecutive Vertices – endpoints that are on same side (back-to-back)
Diagonal – segment that joins 2 nonconsecutive vertices
11.1-Polygon BasicsInterior Angles Theorem
The sum of the interior angles of a convex n-gon is:
(n-2) * 180°Example:
Find the sum of the angles in the figure:
Octagon
11.1-Polygon BasicsExample:
Find the value of x in the figure:
Quadrilateral108
°
x°
121°
59°
11.1-Polygon BasicsExample:
The sum of the measures of the interior angles of a convex polygon is 900°. Classify the
polygon by the number of sides.
11.1-Polygon BasicsExterior Angles Theorem
The sum of the exterior angles of a convex n-gon is:
m<1 + m<2 + … + m<n = 360°
Example:Find the value of x in the figure below:
86°
90°
3x
x