Lesson 1.4 - Polygons

Geometry Homework: Lesson 1.4/1-26 allAssignment from my web page:

View PPT “Conjectures: aka Theorems and Postulates”.Answer the ‘Time to Ponder’ questions/1-16

(on white lined paper-no fringe)Due: Wednesday, October 2

Examples of polygons:

Convex Polygon Concave

Polygon

Not Polygons

Polygon• Means: “many-angled”• A polygon is a closed figure formed

by a finite number of coplanar segments

• Each segment intersects only at each endpoint.

Two Types of Polygons:1. Convex: If diagonals are drawn

from the vertices of a polygon, all will be on the interior of the polygon

2. Concave: If diagonals are drawn from the vertices of a concave polygon, at least one diagonal will be exterior to the polygon.

Visually, the polygon looks caved-in

Polygons are classified according to the number of sides they have.*A polygon must have at least 3 sides

.

Can a slice of pizza be considered a polygon? Explain.

Special Names for Polygons

*n stands for number of sides.

23 23-gon

Naming a Polygon

Polygon ABCDE • Begin at any point• Follow the path of

the polygon either clockwise or counterclockwise

• MUST stay in order– Polygon Names

• DCBAE• AEDCB• CDEAB….

B

A

E

D

C

DiagonalThe diagonal of a polygon is a

line segment linking two non-adjacent vertices.

*The diagonals are indicated with dashed lines.

Adjacent – next to

Diagonals in a PolygonPolygon Number of

diagonalsTriangle (3) 0

Quadrilateral (4) 2

Pentagon (5) 5

Octagon (8)

Decagon (10)

n

…

2

3nn*n stands for

number of sides.

20

35

Equilateral PolygonEquilateral polygons are polygons in which

all sides have equal lengths

Equiangular Polygon

Equiangular polygons are polygons in which all angles have equal measures

Regular Polygon:A regular polygon is a polygon that

is equilateral AND equiangular

Try This

N

GAX

E H