11-3 Polygons

11-3 Polygons

Chapter 11 Lesson 3

What is a polygon?

• A polygon is a simple, closed figure formed by three or more sides.

• Polygons are normally classified by the number of sides they have!

• Notice the sides of the polygons are not curved, never overlap, and are ALWAYS closed!

Multiple Choice

Using the picture for help, determine whether the figure is a polygon. If it is, classify the polygon. DO NOT CHOOSE THE PICTURE AS YOUR ANSWER!

• This is not a polygon.

• This is a polygon. It is a hexagon.

• This is polygon. It is a nonagon.

Multiple Choice

Using the picture to help, determine whether the figure is a polygon. If it is, classify the polygon. DO NOT CHOOSE THE PICTURE AS YOUR ANSWER!

• This is not a polygon.

• This is a polygon. It is a two-gon.

• This is a polygon. It is a curved triangle.

Interior Angles of a Polygon

• The sum of the degree measures of the interior angles of a polygon with n sides is (n - 2)180!

• The visual shows the number of diagonals that can be drawn to connect the nonconsecutive vertices in a polygon!

Notes Example

• Find the sum of the measures of the interior angles of a nonagon.

• Using (n - 2)180:

• (9-2)180 = 1260 degrees.

Multiple Choice

Find the sum of the measures of the interior angles of an 18-gon.

• 3240 degrees

• 2880 degrees

• 3600 degrees

Uhhh... Tessellation?

• A tessellation is a repetitive pattern of polygons that fit together with no overlaps or holes.

• The sum of the measures of the angles where the vertices meet (in the center) is 360 degrees!

Notes Example

• Determine whether or not a tessellation can be created using only regular hexagons. If not, explain.

• Since n = 3 (120 divides 360 evenly), we can use a hexagon to make a tessellation!

Multiple Choice

Determine whether or not a tessellation can be created using only regular pentagons.

• Yes

• No

Multiple Choice

Is the given shape a polygon?

• Yes

• No

Multiple Choice

Find the sum of the measures of the interior angles of a decagon.

• 1800 degrees

• 1440 degrees