Chapter 3
Polygons
3.1 Basic Polygons
I. Properties of a Polygon
A. A plane figure formed by three or more
consecutive segments (sides or laterals)
B. Each side intersects exactly two other
sides at its endpoints.
C. These intersections are called vertices.
D. No three consecutive vertices are
collinear.
II. Types of Polygons
3 sides – triangle
4 sides – quadrilateral
5 sides – pentagon
6 sides – hexagon
7 sides – heptagon
8 sides – octagon
9 sides – nonagon
10 sides – decagon
12 sides – dodecagon
20 sides – icosagon
n sides – n-gon
III. Convex and Concave Polygons
A. Convex – any two points inside of the
polygon can be connected with a
segment that is completely inside the
polygon.
B. Concave – opposite of convex
IV. Regular Polygons
A. Polygons that are both equilateral and
equiangular.
B. Equilateral – all the sides are the same
length
C. Equiangular – all the angles are the
same measure.
D. Perimeter – the distance around a
polygon
Regular Pentagon
Diagonal – a segment connecting two non-consecutive
vertices
3.2 Angles of Polygons
I. Polygon Interior Angle Theorem
5 sides -- pentagon
3 triangles x 180
540°
3.2 Angles of Polygons
I. Polygon Interior Angle Theorem
6 sides -- hexagon
4 triangles x 180
720°
Total number of degrees in a polygon = 180(n – 2)
3.2 Angles of Polygons
I. Polygon Interior Angle Theorem
6 sides -- hexagon
110°
x + 30
4 triangles x 180
95°
720°
122°
103°
x
II. Regular Polygons
180 (n – 2)
180 (3)
540°  5
108°
Each angle of a regular polygon = 180(n – 2)  n
Regular Octagon
180 ( n – 2)
180 ( 6)
1080° 8
135°
III. Polygon Exterior Angle
Theorem
72°
108°
72°
108°
108°
72°
108°
108°
72°
72°
The sum of the measures of the exterior angles of a
polygon is 360°
3.3 Types of Quadrilaterals
I. Parallelogram - quadrilateral with opposite
sides that are parallel and congruent
55°
125°
55°
125°
Opposite angles are equal in measure
II. Rectangle
A parallelogram with four right angles.
III. Rhombus
Parallelogram with four congruent sides
120°
60°
60°
120°
IV. Square
Parallelogram with four congruent sides and
four right angles
A square is a
parallelogram, a
rectangle, and a
rhombus.
V. Trapezoid
A quadrilateral with one pair of parallel sides
3.4 Trapezoids
Parallel sides are called the bases.
Non-parallel sides are called the legs.
I. Special Trapezoids
A. Isosceles Trapezoid
a trapezoid with two congruent sides
110°
70°
Base angles are congruent
110°
70°
I. Special Trapezoids
B. Right Trapezoid
a trapezoid with two right angles
125°
55°
II. Trapezoid Midsegment Theorem
A
25 cm.
MS = (sum of bases)2
B
MS = (25 + 39)2
E
C
32 cm.
39 cm.
MS = (64)2
MS = 32
F
D