6.1 Polygons

What is a polygon?

• A plane figure that meets these 2 conditions:– it is formed by three or more

segments called sides (no 2 sides with a common endpoint are collinear)

- Each side intersects exactly 2 other sides, one at each endpoint.

Example of a Polygon

vertex

side

vertexB

A

E

D

C

Identifying polygons

I J

KL

Not PolygonsB

A

E

C

F

I J

KL

Naming Polygons

vertex

side

vertexB

A

E

D

C

Name a polygon by listing its vertices consecutively

CDEAB or ABCDE

More on naming…

• Polygons are named by the number of sides they have.

Convex vs. Concave

• A polygon is convex if no line containing a side of the polygon does not contain a

point in the interior of the polygon.

Concave

A polygon is concave if when a side is extended, it contains points in the interior of the polygon.

Convex or Concave??

Regular Polygons

• A polygon is regular if it is equilateral (all sides are congruent) and equiangular (all interior angles are congruent).

Diagonals

• Diagonals of a polygon are segments that join 2 nonconsecutive vertices.

Interior angles of a quadrilateral…

Add to 360º

Find angle Q and angle R

70

x2x

80

P

QR

S •80+70+x+2x=360

•150+3x=360

•3x=210

•X = 70

•Angle Q =70

•AngleR is 2(70)=140