1. Chapter 3
Polygons

2. I. Properties of a Polygon
3.1 Basic Polygons
I. Properties of a Polygon
A plane figure formed by three or more consecutive segments (sides or laterals)
Each side intersects exactly two other sides at its endpoints.
These intersections are called vertices.
No three consecutive vertices are collinear.

3. 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

4. III. Convex and Concave Polygons
Convex – any two points inside of the polygon can be connected with a segment that is completely inside the polygon.
Concave – opposite of convex

5. IV. Regular Polygons
Polygons that are both equilateral and equiangular.
Equilateral – all the sides are the same length
Equiangular – all the angles are the same measure.
Perimeter – the distance around a polygon

6. Regular Pentagon

7. Diagonal
– a segment connecting two non-consecutive vertices

9. 3.2 Angles of Polygons I. Polygon Interior Angle Theorem
5 sides -- pentagon
3 triangles
x 180
540°

10. 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)

11. 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

12. II. Regular Polygons 180 (n – 2) 180 (3) 540°  5 108°
Each angle of a regular polygon = 180(n – 2)  n

13. Regular Octagon
180 ( n – 2)
180 ( 6)
1080° 8
135°

14. III. Polygon Exterior Angle Theorem
72°
108°
72°
108°
108°
72°
72°
108°
108°
72°
The sum of the measures of the exterior angles of a polygon is 360°

15. 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

16. II. Rectangle
A parallelogram with four right angles.

17. III. Rhombus
Parallelogram with four congruent sides
120°
60°
60°
120°

18. IV. Square
Parallelogram with four congruent sides and four right angles
A square is a parallelogram, a rectangle, and a rhombus.

19. V. Trapezoid
A quadrilateral with one pair of parallel sides

21. 3.4 Trapezoids Parallel sides are called the bases.
Non-parallel sides are called the legs.

22. I. Special Trapezoids A. Isosceles Trapezoid
a trapezoid with two congruent sides
110°
110°
70°
70°
Base angles are congruent

23. I. Special Trapezoids B. Right Trapezoid
a trapezoid with two right angles
125°
55°

26. II. Trapezoid Midsegment Theorem
MS = (sum of bases)2 A
25 cm. B
MS = ( )2
MS = (64)2
MS = 32
32 cm. E F C D
39 cm.