1. Get a ruler, protractor, and two sheets of copy paper.

2. 6.1 The Polygon Angle – Sum Theorems
Theorem 6.1 – Polygon Angle-Sum Theorem
The sum of the measures of the interior angles of an n-gon is (n – 2) * 180.

3. Finding a Polygon Angle Sum
What is the sum of the interior angle measures of a heptagon?
Sum = (n – 2) * 180
= (7 – 2) * 180
= 5 * 180
= 900°
The sum of the interior angle measures of a heptagon is 900°.

4. Finding a Polygon Angle Sum
What is the sum of the interior angle measurements of a decagon?

5. An equilateral polygon is a polygon with all sides congruent.
An equiangular polygon is a polygon with all angles congruent.
A regular polygon is a polygon that is both equilateral and equiangular.
Regular Polygon
Equilateral Polygon
Equiangular Polygon

6. Corollary to the Polygon Angle-Sum Theorem
The measure of each interior angle of a regular n-gon is

7. Using the Polygon Angle-Sum Theorem
What is the measure of each interior angle in one hexagonal facet?

8. Using the Polygon-Angle Theorem
What is the measure of angle Y in pentagon TODAY?

9. Using the Polygon-Angle Theorem

10. Exterior Angles
You can draw exterior angles at any vertex of a polygon.

11. Polygon Exterior Angle-Sum Theorem
The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

12. Finding an Exterior Angle Measure
What is the measure of angle 1 in the regular octagon?

13. 6.2 Properties of Parallelograms
A parallelogram is a quadrilateral with both pairs of opposite sides parallel.
In a quadrilateral, opposite sides do not share a vertex and opposite angles do not share a side.

14. Finding an Exterior Angle Measure
What is the measure of an exterior angle for a pentagon?

15. Theorem 6.3
If a quadrilateral is a parallelogram, then its opposite sides are congruent.

16. Consecutive Angles
Angles of a polygon that share a side are consecutive angles.

17. Theorem 6.4
If a quadrilateral is a parallelogram, then its consecutive angles are supplementary.

18. Theorem 6.5
If a quadrilateral is a parallelogram, then its opposite angles are congruent.

19. Example 1
What are the measures of angles B, C, and D?

20. Theorem 6.6
If a quadrilateral is a parallelogram, then its diagonals bisect each other.

21. Using Algebra to Find Lengths
Solve a system of linear equations to find the values of x and y in parallelogram KLMN. What are KM and LN?

22. Using Algebra to Find Lengths