1. Chapter 6 Section 6.1
Polygons

2. 180o
3x = 180
3x + 87 = 180
3x = 93
x = 31
Equilateral
Equiangular

3. Examples of Polygons Identify, Name, and Describe Polygons Definition
Definition Polygon
A polygon is a plane figure that is formed by three or more
segments called sides, such that no two sides with a
common endpoint are collinear, and each side intersects
exactly two other sides, one at each endpoint. Each
endpoint is called a vertex of the polygon
Examples of Polygons

4. No: All sides must be straight
Identify, Name, and Describe Polygons
No: All sides must be straight
No: All sides must be straight
Yes

5. Identify, Name, and Describe Polygons
Names
Names Polygon Names
A polygons name depends on the number of sides it has
# of Sides
Name 3
Triangle 4
Quadrilateral 5
Pentagon 6
Hexagon 7
Heptagon
# of Sides
Name 8
Octagon 9
Nonagon 10
Decagon 12
Dodecagon N
N-gon

6. Non-Convex/Concave: A polygon that is not convex
Identify, Name, and Describe Polygons
Descriptions
Descriptions Describing Polygons
A polygons description depends on its shape
Convex: No line that contains a side of the polygon contains a point in the interior of the polygon
Non-Convex/Concave: A polygon that is not convex
Examples

7. Hexagon Concave Heptagon Heptagon Concave Convex
Identify, Name, and Describe Polygons
Hexagon
Concave
Heptagon
Heptagon
Concave
Convex

8. Identify, Name, and Describe Polygons
Heptagon
BCDEFGA DEFGABC

9. Identify, Name, and Describe Polygons
C, D, E, F

10. Identify, Name, and Describe Polygons

11. Sum interior angles of a quadrilateral
Theorem
Theorem 6.1 Interior Angles of a Quadrilateral
The sum of the measures of the interior angles of a
quadrilateral is 360o
mH + mG + mF + mE = 360o

12. Sum interior angles of a quadrilateral
(x + 15) + (x + 15) + (2x) + (2x) = 360
6x + 30 = 360
6x = 330
x = 55

13. Sum interior angles of a quadrilateral
(5x - 15) + (3x - 1) + (4x + 34) + (5x - 15) = 360
17x + 3 = 360
17x = 357
x = 21

14. Sum interior angles of a quadrilateral
(4x - 15) + (5x + 11) + (6x + 19) + (5x + 5) = 360
20x + 20 = 360
20x = 340
x = 17

15. HW #66 Pg 325-328 12-20 Even, 21-23, 24-38 Even 42-52 Even