Warm Up 1. How many sides do the following figures have? b) a) 2. Solve for x. 50 2x - 12 b) a) 35 2x + 7

Section 1.6 Classifying Polygons

A Polygon is a closed plane figure with the following properties: What is a Polygon? A Polygon is a closed plane figure with the following properties: 1) Is formed by 3 or more line segments (sides) 2) Each side intersects exactly 2 sides, but only at their endpoints

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.)

convex concave A Polygon can either be convex or concave. no sides go through the interior of the polygon. convex concave A side goes through the interior of the polygon.

Which figures are polygons? Example 1: Which figures are polygons?

Which figures are polygons? Example 1: Which figures are polygons? polygon polygon polygon polygon

Label the polygons as convex or concave? Example 2: Label the polygons as convex or concave?

Label the polygons as convex or concave? Example 2: Label the polygons as convex or concave? convex concave concave convex

Parts of a polygon Vertices Interior Angles Exterior Angles Area Sides The 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 Area Sides Perimeter

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

Amount of surface covered by a figure Parts of a polygon Area Amount of surface covered by a figure

In more complex polygons there are more parts. Learn these new terms: Parts of a polygon In more complex polygons there are more parts. Learn these new terms: Consecutive Diagonal Regular

Parts of a polygon Consecutive (side/angles) Refers to parts that are right next to each other. (They share a common vertex or side.) )

Parts of a polygon Diagonal A segment that joins two nonconsecutive vertices. (Notice the triangle does NOT have any diagonals.)

A convex polygon that is equilateral and equiangular. Parts of a polygon Regular A convex polygon that is equilateral and equiangular. ) )

A Polygon is classified by its’ number of sides. Type of Polygon 12 n 9 10 4 3 8 5 6 7 Pentagon Quadrilateral Hexagon Triangle n - gon Dodecagon Decagon Nonagon Octagon Heptagon

A Polygon is classified by its’ number of sides. 3 4 5 10 7 8 9 6 11 n-gon : can be used to name a polygon n = number of side ex: 100-gon -refers to a polygon with 100 sides What do you notice as n gets bigger?

Examples Name each polygon by its number of sides. Then classify it as convex or concave and equilateral, equiangular, or regular. 4 )

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