Honors Geometry
Name:________________________
3.5 Class Notes Polygons
Date:_________________Pd:______
What makes a polygon?
A polygon is ___________________________________________________________________________
1. the sides that have a common endpoint are noncollinear, and
2. each side intersects exactly two other sides, but only at their endpoints.
Examples of Polygons
Figures that are Not Polygons
Convex Polygon: A polygon such that no line containing a side of the polygon contains a point in the interior of the
polygon.
 A polygon that is not convex is nonconvex or concave.
Diagonal: A segment joining two nonconsecutive vertices.
Draw the diagonals from one vertex.
# sides:
# sides:
# triangles formed:
# triangles formed:
# sides:
# triangles formed:
An n-gon would form ______________________ triangles from its diagonals from one vertex.
The interior angle sum of a quadrilateral is _________________.
Look at the diagrams above and create a formula for the interior angle sum of a convex polygon:
Theorem 3-13: The sum of the measures of the angles of a convex polygon with n sides is
__________________________.
Draw 3 different convex polygons. Draw the exterior angles. What happens to the angles as polygons have more sides?
What do you think this does to the exterior angle sum?
Theorem 3-14: The sum of the measures of the exterior angles of any convex polygon, one
angle at each vertex, is _______________________.
Regular Polygon: A polygon that is both __________________ and __________________.
*A triangle is the simplest polygon. The terms applied to triangles, such
as vertex and exterior angle also apply to other polygons.
Complete the table:
Number of Sides
3
4
5
6
7
8
9
10
12
n
Name
Interior Angle Sum
Practice…
Complete each statement with always, sometimes, or never.
1.)
The sum of the measures of the exterior angles of any polygon, one angle at each vertex,
is ____________________ 360o
2.)
The sum of the measure of the angles of a convex polygon is ____________________360 o.
3.)
A segment joining two vertices is ____________________ a diagonal.
4.)
The sum of the measures of the exterior angles of a polygon ____________________ depends on the number of sides of
the polygon.
5.)
A regular polygon is ____________________ equilateral.
6.)
An equiangular polygon is ____________________ regular
Find the interior angle sum and the exterior angle sum for:
7.)
a triangle
8.)
a 20-gon
9.)
a 27-gon
Complete.
10.)
An exterior angle of a regular polygon has measure 10. The polygon has _______ sides.
11.)
An interior angle of a regular polygon has measure 160o. They polygon has _____ sides.
12.)
Three of the angles of a quadrilateral have measures 90o, 60o, and 115o. The fourth angle has measure _______o.
13.)
The sum of the measures of the interior angles of a polygon is five times the sum of the
measures of its exterior angles, one angle at each vertex. How many sides does the polygon have?
14.)
Six angles of a convex octagon are congruent. Each of the other two angles has a measure of 20 more than the
measure of each of the other six angles. Find the measure of each angle.
HW: Page 24# 9 – 25 ODD