1. Bell work: Find the range of possible values for each variable
6, 6, and x as the side lengths of a triangle

2. 6-1: The Polygon Angle Sum Theorem

3. Partner Work
With a partner, determine the total sum of the interior angles for a square, a hexagon, and an octagon (4, 6, and 8 sides). You can do this by measuring, estimating, or any other method you’d like, but be prepared to justify your answer.
Once you’ve done this, make a conjecture (without drawing or measuring) on the sum of the angles of a decagon (10 sides)

4. What is the sum of the interior angles of a heptagon? (7 sides)
What is the sum of the interior angles of a 17-gon?

5. The sum of all the interior angles of a polygon is 1980…how many sides does the shape have?

6. What is the sum of the interior angles of a 35-gon?
How many sides does the polygon with interior angle sum equal to have?

7. Notes
Theorem 6.1: The sum of the measures of all the interior angles of a polygon with n- sides is (n-2) x 180 degrees
An Equilateral Polygon has all sides equal
An Equiangular Polygon has all angles equal
A Regular Polygon is equilateral and equiangular

8. Find the measure of one interior angle to the regular polygon

9. What would the total sum of the EXTERIOR angles for a square, a pentagon, and a hexagon (4, 5, and 6 sides) be?. You can do this by measuring, estimating, or any other method you’d like, but be prepared to justify your answer.
Once you’ve done this, make a conjecture (without drawing or measuring) on the sum of the angles of a decagon (10 sides)

10. Notes
Corollary to theorem 6.1: The measure of each interior angle of a REGULAR n-gon = 𝑛−2 180 𝑛
Theorem 6.2: The sum of the measures of the exterior angles of any polygon is 360

11. What is the measure of each interior angle in a regular hexagon?
What is the measure of each interior angle in a regular nonagon?

12. Find the measure of angle Y

13. Find the measure of angle G

14. What is the sum of the measures of the exterior angles of a 225-gon?
Find the measures of an interior angle and an exterior angle for a regular dodecagon (12 sides)

15. Chapter 5 Review

16. One row at a time, get a white board, marker, and eraser from the front of the class
Show your work for all problems
Any non-math related drawings will result in a loss of whiteboard privileges…

17. Vocab Perpendicular Bisector Circumcenter Incenter Angle Bisector
Median
Altitude
Circumcenter
Incenter
Centriod
Orthocenter
Midsegment

18. Draw 3 triangles
…now, construct an altitude, median, and circumcenter, one in each triangle (and identify it)

19. List the sides of the triangle from shortest to longest.

22. Find the value of X

23. Homework Study for a chapter 5 quiz on Friday
Section 6.1, page : 7, 10, 12, 16, 20, 23
Honors: Add 11, 17, 29, 32,