POLYGONS

What is a polygon

• 2-D figure formed by connecting segments endpoint to endpoint

Parts• Segment called a side• Vertex is point where two sides meet • Diagonal is a segment that connects two

vertices that aren't a side

side

Diagonal

vertex

Parts• Interior angle is an angle formed by two

adjacent sides inside the polygon.• Exterior angle is an angle formed by two

adjacent sides outside the polygon.

Interior angle

Exterior angle

Types

• Convex has no diagonal outside the polygon

• Concave has at least one diagonal is outside the polygon

• Hint: caved in.

Types• Equilateral has all sides the same

length• Equiangular has all angles the

same degrees

6

6

6

6 120o

120o 120o

120o

120o120o

• Regular is equilateral and equiangular

6

6

6

6

Properties• Congruent polygons are exactly the same

size and shape

How to Name• Polygons are named by their vertices listed the

consecutive order going around the polygon

N C

I

L

SA

P

E

U C

H

Y

BZ

M

O

Octagons MOUCHYBZ & PENCILSA

How to Name• Polygons are named by the number of sides

Number sides Name

3 tri- Triangle

4 quad- Quadrilateral

5 penta- Pentagon

6 hexa- Hexagon

7 hepta- Heptagon

8 octa- Octagon

9 nona- Nonagon

10 deca- Decagon

11 undeca- Undecagon

12 dodeca- Dodecagon

10 or more n-gon

12

453

2

1

13

121110

9

8

7

6

More Naming• 3= tri 4= tetra

5= penta 6= hexa or sexa 7= hepta

8= octa 9= nona or ennea 10= deca

11= undeca or

hendeca 12= dodeca 13= triskaideca

14= tetradeca 15= pentadeca 16= hexadeca

17= heptadeca 18= octadeca 19= enneadeca

20= icosa30= triaconta 40= tetraconta

50= pentaconta 60= hexaconta 70= heptaconta

80= octaconta 90= enneaconta 100= hecto

TOTAL ANGLE MEASURE

• Formula 2 180TAM ( )n

• 32-gon 32 2 180TAM ( )

30 180( )

5400

INTERIOR ANGLE MEASURE

• Formula 2 180( )IAM

n

n

• 20-gon 20 2 180

20

( )IAM

18 180

20

( ) 162

EXTERIOR ANGLE MEASURE

• Formula360

EAMn

• 18-gon 20360

18EAM

Number of Diagonals(Convex)

2

)3( nn