Geometry B Name:______________________ Date: ___________

Chapter 6: Polygons and Quadrilaterals

Section 6.1: Properties and Attributes of Polygons

DO NOW

1. A ___________ is a three-sided polygon.

2. A ____________ is a four-sided polygon.

Evaluate each expression for n = 6.

3. (n – 4) 12 4. (n – 3) 90

Solve for a.

5. 12a + 4a + 9a = 100

Objectives of Lesson: ________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

When would I ever use this? The opening that lets light into a camera lens is

created by an aperture, a set of blades whose edges may form a polygon.

Each segment ______________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

2

Number of

sides

Name of Polygon Number of

sides

Name of Polygon

Remember_________________________________________________

_________________________________________________________

_________________________________________________________

Example 1: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number

of sides.

Example 2: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number

of sides.

Example 3: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number

of sides.

3

Example 4: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number

of sides.

Example 5: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number

of sides.

Example 6: Identifying Polygons

Tell whether the figure is a polygon. If it is a polygon, name it by the number

A regular polygon ___________________________________________

_________________________________________________________

_________________________________________________________

A polygon is concave__________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

Example 7: Classifying Polygons

Tell whether the polygon is regular or irregular. Tell whether it is concave or

convex.

4

Example 8: Classifying Polygons

Tell whether the polygon is regular or irregular. Tell whether it is concave or

convex.

Example 9: Classifying Polygons

Tell whether the polygon is regular or irregular. Tell whether it is concave or

convex.

Example 10: Classifying Polygons

Tell whether the polygon is regular or irregular. Tell whether it is concave or

convex.

Example 11: Classifying Polygons

Tell whether the polygon is regular or irregular. Tell whether it is concave or

convex.

To find the sum of the interior angle measures of a convex polygon, draw all

possible diagonals from one vertex of the polygon. This creates a set of

triangles. The sum of the angle measures of all the triangles equals the sum

of the angle measures of the polygon.

5

Remember________________________________________________

_________________________________________________________

_________________________________________________________

Polygon Number of Sides Number of Triangles Sum of Interior

Angle Measures

_________________________________________________________

_________________________________________________________

_________________________________________________________

_________________________________________________________

Polygon Angle Sum Theorem

Example 12: Finding Interior Angle Measures and Sums in Polygons

Find the sum of the interior angle measures of a convex heptagon.

Example 13: Finding Interior Angle Measures and Sums in Polygons

Find the measure of each interior angle of a regular 16-gon.

6

Example 14: Finding Interior Angle Measures and Sums in Polygons

Find the measure of each interior angle of pentagon ABCDE.

Example 15: Find the sum of the interior angle measures of a convex 15-gon.

Example 16: Find the measure of each interior angle of a regular decagon.

In the polygons below, an exterior angle has been measured at each vertex.

Notice that in each case, the sum of the exterior angle measures is 360°.

7

Remember________________________________________________

________________________________________________________

Polygon Exterior Angle Sum Theorem

Example 17: Finding Interior Angle Measures and Sums in Polygons

Find the measure of each exterior angle of a regular 20-gon.

Example 18: Finding Interior Angle Measures and Sums in Polygons

Find the value of b in polygon FGHJKL.

Example 19: Find the measure of each exterior angle of a regular dodecagon.

Example 20: Find the value of r in polygon JKLM.

8

Example 21: Art Application

Ann is making paper stars for party decorations. What is the measure of 1?

Example 22: Photography Application

The aperture of the camera is formed by ten blades. The blades overlap to

form a regular decagon. What is the measure of ∠CBD?

Example 23: Photography Application

What if…? Suppose the shutter were formed by 8 blades instead of 10

blades. What would the measure of each exterior angle be?

smilardo.wordpress.com - homework: worksheets: link to book and more

Twitter @MsMilardo