Warm Up 1. How many sides do the following figures have? a) b) 2. Solve for x. 352x + 7 50 2x - 12 a) b)

Warm Up

1. How many sides do the following figures have?

a) b)

2. Solve for x.

352x + 7

50 2x - 12

a) b)

Section 1.6

Classifying Polygons

A Polygon is a closed plane figure with the following properties:

What is a Polygon?

1) Is formed by 3 or more line segments (sides)

2) Each side intersects exactly 2 sides, but only at their endpoints

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.)

A Polygon can either be convex or concave.

A Polygon can either be convex or concave.

convex

• no sides go through the interior of the polygon.

• A side goes through the interior of the polygon.

concave

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 polygon

Vertices – each endpoint of a side

Parts of a polygon

Interior Angles

)

)

)

)

)

)

)

)

))

)

Parts of a polygon

Exterior Angles

Parts of a polygon

Sides

Parts of a polygon

Perimeter

Add all sides

Parts of a polygon

Area

Amount of surface covered by a figure

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

Diagonal RegularConsecutive

Parts of a polygon

Refers to parts that are right next to each other.

(They share a common vertex or side.)

Consecutive (side/angles))

)

Parts of a polygon

Diagonal

A segment that joins two nonconsecutive vertices.(Notice the triangle does NOT have any diagonals.)

Parts of a polygon

A convex polygon that is equilateral and equiangular.)

)

)

)

)

))

))

)

)Regular

A Polygon is classified by its’ number of sides.

3

4

5

6

7

8

9

10

12

n n - gonDodecagon

Decagon

Nonagon

Octagon

Heptagon

Hexagon

Pentagon

Quadrilateral

Triangle

Number of Sides Type of Polygon

A Polygon is classified by its’ number of sides.

ex: 100-gon -refers to a polygon with 100 sides

• n-gon : can be used to name a polygon n = number of side

3 4 5

10

78 9

6

11

What do you notice as n gets bigger?

ExamplesName each polygon by its number of sides. Then classify it as convex or concave and equilateral, equiangular, or regular.

4

4 4

4

)

)

))

)

)

))

Tell Whether the statement is always, sometimes, or never true.

Examples

A regular polygon is equiangular.

A triangle is convex.

A regular polygon is equilateral.

Example

The expression (-2x + 41) and (7x - 40) represent the lengths of two sides of a equilateral pentagon. Find the side of the pentagon.

Example

The expression (9x + 5) and (11x - 25) represent the measures of two angles of a regular nonagon. Find the measure of angle of the nonagon.

Homework

Workbook p16#’s 1-23 odd