1. Happy Wednesday!!

2. 11.1-Polygon Basics
polygon “poly” = many…and “gon” = sides So a polygon is a closed shape with 3 or more sides. Examples: Triangle Rectangle Hexagon

3. Every polygon has the same features:
11.1-Polygon Basics
Every 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°)

4. 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

5. 11.1-Polygon Basics Special 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

6. Interior Angles Theorem
11.1-Polygon Basics
Interior 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

7. Example: Find the value of x in the figure:
11.1-Polygon Basics
Example: Find the value of x in the figure:
108°
121°
Quadrilateral x°
59°

8. 11.1-Polygon Basics
Example: The sum of the measures of the interior angles of a convex polygon is 900°. Classify the polygon by the number of sides.

9. 11.1-Polygon Basics
Exterior 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° x
90° 3x