1. Things Needed Today (TNT):
Math CC7/8 – Sept. 12
Things Needed Today (TNT):
Math Notebook/Pencil
Math Book –Shapes & Designs 2.1 pg. 41
Shape Set sheet (located on table)
Angle ruler
Math Notebook
Topic: Angle Sums of Regular Polygons
HW: S &D pg #1-2, 17, 18 (#22 is optional)

2. What’s Happening? Warm Up Lesson- S&D 2.1!
Develop properties of polygons

3. Warm-Up Find the value of n Estimate the answers Find the mean
WRITE down each problem & SOLVE
Show ALL your work & THINKING
Find the mean
16, 21,18, 15, 20
Find the value of n
2) 8(n) = n = ?
3) n •11 = n = ?
4) 7(12) = n n = ?
Estimate the answers
5) ≈ ≈
821 – 393 ≈
8) Make a list of all the factors of 24

4. Warm-Up Answers 18 Find the value of n Estimate the answers
WRITE down each problem & SOLVE
Show ALL your work & THINKING
Find the mean
16, 21,18, 15, 20 18
Find the value of n
2) 8(n) = n = 9
3) n •11 = n = 10
4) 7(12) = n n = 84
Estimate the answers
5) ≈ 800
≈ 1400
821 – 393 ≈ 400
8) Make a list of all the factors of , 2, 3, 4, 6, 8, 12, 24

5. We will develop properties of polygons.
Shapes & Designs, p. 41
Designing Polygons:
The angle Connection
We will develop properties of polygons.
These properties make polygons useful in many natural objects like the combs made by bees to store their honey.

6. 2.1 Angle Sums of Regular Polygons
Polygons with the same number of sides can have different shapes. However, there is an important relationship between the # of sides and the angle sum of any polygon.
You will develop a formula that relates the number of sides to angle measures.

7. Regular Polygon
Take Notes
A Regular Polygon is a polygon in which ALL sides are the same length and ALL of the angles have the same measure.

8. Irregular Polygon
Take Notes
In an Irregular Polygon, NOT all of the sides are the same length or NOT all of the angles have the same measure.

9. Polygons are named based on the number of sides and angles they have.
How are polygon named?
Polygons are named based on the number of sides and angles they have.
Example: a polygon with 6 sides and 6 angles is called a hexagon.
Polygon with 8 sides and 8 angles:

10. Look at the 6 examples of polygons from the Shape Set.
Study these examples to find a relationship between the number of sides and angles.
Is there a relationship between the size of the angles and the number of sides for a Regular Polygon?

11. Problem 2.1 1. Enter the results in the table (class worksheet)
You can discover relationships between the number of sides and the angle measures of polygons. Measure some examples, organize the data, and then look for patterns.
Problem 2.1 A
Use an angle ruler to measure the angles in the equilateral triangle, the square, the regular pentagon, and the regular hexagon from the Shapes Set.
1. Enter the results in the table (class worksheet)

12. Check your work 3 4 5 6 7 8 9 10

13. Problem 2.1 continued 2
Find a pattern that suggests a way to fill in the table for regular polygons with 7, 8, 9 and 10 sides. Then measure the angles of the Shape Set heptagon and octagon. Does your pattern holds in those cases?
Describe a pattern relating angle sums to the number of sides in regular polygons. 3
As the number of sides increases by 1, the angle sum increases by 180 degrees.

14. Describe a pattern relating measures of individual angles and number of sides in regular polygons.4
As the number of sides increases, each individual angle measure increases.

15. Yes, the pattern still applies
Yes, the pattern still applies! The “LENGTH” of sides does NOT have any bearing on the size of the angle.

16. A = 180 (n – 2) n S = 180 (n - 2) or S = 180n - 360 A = 180n – 360
S= the total sum of the interior angles of a regular polygon
A = 180 (n – 2) n
A = 180n – 360 n
A = n or or
A= the measure of each individual angle of the regular polygon

17. If time start your HW p. 52 # 1-2, 17, 18 (#22 is optional)