1. Chapter 5: Properties of Polygons
Objective:
Discover relationships among the sides, angles, and diagonals of polygons
Study the properties of polygons
Use polygons to solve problems

2. Polygon terms we know: Polygons Descriptors or parts Pentagon
Quadrilateral
Pentagon
Concave
Trapezoid
Convex
Hexagon
Kite
Octogon
Rectangle
Vertex
Side
Square
Diagonal
Regular Polygon

3. Polygon Sum Conjecture
Objective:
Write a conjectures about the sum of the angle measures of a polygon

4. 1. Draw 2 of your assigned polygon.
2. Measure and label all interior angles.
3. Find the sum of all interior angles.
4. Compare your results with person sitting next to you.
The sum of the measures of the n interior angles of an n-gon is ______________.
Polygon Sum Conjecture
1800 (n – 2) ?
. . .
Sum of interior angles n 8 7 6 5 4 3
# of sides of polygon
1800
3600
5400
7200
9000
10800
1800
+ 1800
+ 1800
+ 1800
180(3) + ______= 180
180(3) + 180(-2) = 180
180 (3 – 2) = 180
-360
( – 2) n
nth term:

5. a + b + c = 1800
x + y + z = 1800 x a
Triangle Sum Conjecture y
(a + b + c) + (x + y + z) = 3600 b
Addition Property of equality
Sum of the measures of the interior angles of a quadrilateral equals 3600 c z
Pg 257 #1-14, 16

6. Count the triangles you made it is clear to see,
Take a point on your poly as a place to start. Draw the lines to the corners, a work of art. (The poly, the poly, the poly formula)
Count the triangles you made it is clear to see,
there are 2 less than sides or vertices.
(The poly, the poly, the poly formula)
180 is the count of each triangle you draw
Add them all together for the total sum law
(The poly, the poly, the poly formula)

7. There is more to the story than what’s inside
The sum of all angles for a polygon you do is the product of 180 and (n - 2)
There is more to the story than what’s inside
For the outside use 360 as your guide
Inside and outside a linear pair
all sides the same makes it regular.
There’s a special rule for the exterior:
Sides and angles are the same: it is regular

8. Inside and outside a linear pair all sides the same makes it regular
360 divided by sides gives each angle 360 divided by angles gives each side
Inside and outside a linear pair
all sides the same makes it regular
The next thing to do is to find a side
When the angle just happens to be inside.
Subtract it form 180 (it’s a linear pair)
Use the rule above now its exterior!

9. The last thing to do is a quick review
Study, do you classwork, its up to you!
The sum of all angles for a polygon you do is the product of 180 and (n - 2) The product of 180(n – 2)
There’s a special rule for the exterior: 360 divided by sides gives each angle 360 divided by angles gives each side
Inside and outside a linear pair
all sides the same makes it regular.