Post on 05-Feb-2018
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