1. NAMING
POLYGONS

2. What does the word “polygon” mean?
Let's Discuss
What does the word “polygon” mean?
What is the smallest number of sides a polygon can have?
What is the largest number of sides a polygon can have?

3. Triangle
Octagon
Quadrilateral
Nonagon
Pentagon
Decagon
Dodecagon
Hexagon
n-gon
Heptagon

4. Hip Bone’s connected to the… Classifying Polygons
Polygons with 3 sides… Triangles
Polygons with 4 sides… Quadrilaterals
Polygons with 5 sides.. Pentagons
But wait we have more polygons
Polygons with 6 sides… Hexagons
Polygons with 7 sides… Heptagons
Polygons with 8 sides… Octagons
But still we have more polygons
Polygons with 9 sides… Nonagons
Polygons with 10 sides… Decagons
Polygons with 12 sides… Dodecagons
And now we have our polygons

5. Important Terms A VERTEX is the point of intersection of two sides F A
CONSECUTIVE VERTICES are two endpoints of any side. F A B C D E
A segment whose endpoints are two
nonconsecutive vertices is called a DIAGONAL.
Sides that share a vertex are called CONSECUTIVE SIDES.

6. More Important Terms EQUILATERAL - All sides are congruent
EQUIANGULAR - All angles are congruent
REGULAR - All sides and angles are congruent

7. Polygons are named by listing its vertices consecutively.F E D

8. Polygons can be CONCAVE or CONVEX

9. Ex. 3 Classify each polygon as convex or concave.

10. Diagonals &
Angle Measures

11. What is the sum of the measures of the interior angles of a triangle?
REVIEW:
What is the sum of the measures of the interior angles of a triangle?
180°
180°
180°
What is the sum of the measures of the interior angles of any quadrilateral?
360°

12. Sum of measures of interior angles
# of triangles
Sum of measures of interior angles
# of sides
1(180) = 180 3 1
2(180) = 360 4 2 3
3(180) = 540 5 6 4
4(180) = 720
n-2
(n-2) 180 n

13. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180°)

14. Ex. 1 Use the regular pentagon to answer the questions.
Find the sum of the measures of the interior angles.
Find the measure of ONE interior angle
540°
108°

15. Two more important terms
Interior Angles
Exterior Angles

16. 1 2 3 4 5
If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°.

17. If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°.1 3 2

18. If any convex polygon, the sum of the measures of the exterior angles, one at each vertex, is 360°.1 2 4 3

19. Ex. 2 Find the measure of ONE exterior angle of a regular hexagon.
60°

20. Ex. 3 Find the measure of ONE exterior angle of a regular heptagon.
51.4°

21. Ex. 4 Each exterior angle of a polygon is 18
Ex. 4 Each exterior angle of a polygon is 18. How many sides does it have?
n = 20

22. Ex. 5 The sum of the measures of five interior angles of a hexagon is What is the measure of the sixth angle?
185°

23. Ex. 6 The measure of the exterior angle of a quadrilateral are x, 3x, 5x, and 3x. Find the measure of each angle.
30°, 90°, 150°, and 90°

24. Ex. 7 If each interior angle of a regular polygon is 150, then how many sides does the polygon have?
n = 12

25. Practice Time
Practice Worksheet 10-2

26. Homework:
Page 406 # even
Page 411 # 8-18 all

27. Foldable for Formulas Sum of INTERIOR Angles ONE INTERIOR Angle Sum
EXTERIOR
Angles
ONE
EXTERIOR
Angle