Polygon 1.6 Power Point Guide (Poly – means “many”) Examples: So…a polygon is a many sided closed figure.

1.6 Power Point Guide

Let’s categorize….. (dents/no dents)

A closed figure that is “many” sided A type of polygon with no dents A type of polygon with dents (“think cave”)

EXAMPLE 1 Identify polygons Tell whether the figure is a polygon and whether it is convex or concave. a. b. c. d. SOLUTION Some segments intersect more than two segments, so it is not a polygon. a. b. The figure is a convex polygon. Part of the figure is not a segment, so it is not a polygon. c. d. The figure is a concave polygon.

# of sides Type of Polygon triangle quadrilateral pentagon hexagon heptagon octagon nonagon decagon dodecagon n-gon 3 4 5 6 7 8 9 10 12 n What is a polygon with 199 sides called? 199-gon

All the sides are equal and all the interior angles are equal. All sides are equal. All the interior angles are equal. Think “lateral” – like a lateral pass in football Here are some examples:

EXAMPLE 2 Classify polygons Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. a. b. SOLUTION The polygon has 6 sides. It is equilateral and equiangular, so it is a regular hexagon. a. The polygon has 4 sides, so it is a quadrilateral. It is not equilateral or equiangular, so it is not regular. b.

EXAMPLE 2 Classify polygons Classify the polygon by the number of sides. Tell whether the polygon is equilateral, equiangular, or regular. Explain your reasoning. c. c. The polygon has 12 sides, so it is a dodecagon. The sides are congruent, so it is equilateral. The polygon is not convex, so it is not regular.

EXAMPLE 3 Find side lengths A table is shaped like a regular hexagon.The expressions shown represent side lengths of the hexagonal table. Find the length of a side. ALGEBRA SOLUTION First, write and solve an equation to find the value of x. Use the fact that the sides of a regular hexagon are congruent. 3x + 6 4x – 2 = Write equation. 6 = x – 2 Subtract 3x from each side. 8 = x Add 2 to each side.

EXAMPLE 3 Find side lengths Then find a side length. Evaluate one of the expressions when x = 8. 30 3(8) + 6 = 3x + 6 The length of a side of the table is 30 inches. ANSWER

GUIDED PRACTICE for Example 3 The expressions 8y° and ( 9y – 15 )° represent the measures of two of the angles in the table in Example 3. Find the measure of an angle. 3. SOLUTION First , write and solve an equation to find the value of y. Use the fact that that the angles of a regular hexagon are congruent. 8y = 9y – 15 Write equation 0 = y – 15 Subtract each side by 8y 15 = y Add 15 to each side

GUIDED PRACTICE for Example 3 Then find an angle. Evaluate one the expression when y = 15° 8y = 8 · 15° = 120° The measure of an angle is 120° ANSWER

Fly Swatter Game!!!! Fly swatter is a speed game that involves speed thinking and speed swatting. Here is how the game works: The first person from each team comes up and stand behind the white line. Once I read the question the first person to swat the correct answer wins a point for their team (you can swat once!) There will be no pushing or shoving someone to try a swat an answer first. Also, no yelling out answers. If any of this happens the guilty team will be deducted 1 point. The next two people will stand behind the line and the process repeats. The team with the most amount of points at the end wins. 1pt correct swat 1 pt correct explanation

Question 1

The answers two the following two questions are the same 1 and 2 are what kind of adjacent angles? A and B are what kind of non-adjacent angles? A B

Question 2

F and G are what kind of angles?

Question 3

AED and BEC are what kind of angles?

Question 4

AEB and BEC form a what?

Question 5

Find a concave hexagon.

Question 6

These are all what kind of polygons?

Question 7

Name this polygon based on the number of sides it has.

Question 8

What is the term for polygons where all the ’s are congruent, but the sides are not necessarily equal?

Question 9

Name this polygon based on the number of sides it has.

Question 10

This is what type of quadrilateral?

Question 11

This is a _______ quadrilateral.

Question 12

Find a convex heptagon

Question 13

What is the special name for a polygon with an unknown number of sides?

Question 14

Find a convex nonagon

Question 15

Base on the number of sides name this polygon.

Question 16

Name this concave polygon.