6.1 Exploring Polygons

Created by Cathy and Jim Carroll

•Convex and Concave Polygons

•Parts of a Polygon•Classifying Polygons

Convex or Concave?A Polygon is a plane figure formed by three or more segments.A Polygon can either be convex or concave.

If a polygon is convex then no sides go through the interior of the polygon.

(All vertices point outside the polygon.)

If a polygon is concave then it is not convex. A side goes through the interior of the polygon. (At least one vertex points inside the polygon.)

Example 1:Which figures are polygons?

Example 1:Which figures are polygons?

polygon polygon polygon

polygon

Example 2:Label the polygons as convex or concave?

Example 2:Label the polygons as convex or concave?

convex concave concave convex

Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.Vertices Interior Angles Exterior Angles

Perimeter AreaSides

Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.Vertices

Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.Vertices Interior Angles

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Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.Vertices Interior Angles Exterior Angles

Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.Vertices Interior Angles Exterior Angles

Sides

Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.Vertices Interior Angles Exterior Angles

Perimeter

Add all sides

Sides

Parts of a polygonThe simplest polygon is a triangle. Many of the terms you learned about a triangle apply to all polygons. Remind yourself of what the following terms mean.Vertices Interior Angles Exterior Angles

Perimeter AreaSides

Parts of a polygonIn more complex polygons there are more parts.Learn these new terms:

Diagonal RegularConsecutive

Parts of a polygonIn more complex polygons there are more parts.Learn these new terms:

Refers to parts that are right next to each other.(They share a common vertex or side.)

Diagonal RegularConsecutive

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Parts of a polygonIn more complex polygons there are more parts.Learn these new terms:

Diagonal RegularConsecutive

Joins two nonconsecutive vertices.(Notice the triangle does NOT have any

diagonals.)

Parts of a polygonIn more complex polygons there are more parts.Learn these new terms:

A polygon that is equilateral and equiangular.)

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Diagonal RegularConsecutive

Classifying Polygons

A Polygon is classified by its’ number of sides.

34567891012n n - gon

DodecagonDecagonNonagonOctagonHeptagonHexagonPentagon

QuadrilateralTriangle

Number of Sides Type of Polygon

Example:The perimeter of the pentagon is 20. Solve for X.

X+1 2X

2X-1

X + 6

X

Remember what perimeter means

The Sum of all the sides

Example:The perimeter of the pentagon is 20. Solve for X.

X+1 2X

2X-1

X + 6

X

(X+ 1) + (2X) +(X) + (2x-1) + (x+6 )= 20

Combine like terms and solve

7X + 6 = 207 X = 14X = 2

THE ENDIf you need more help, try:

• Your textbook

• The DVD station

• Your partner

• A Peer Tutor

• The teacher