1. Sect. 6.1 Polygons Goal 1 Describing Polygons Goal 2 Interior Angles of Quadrilaterals

2. Describing Polygons Polygon: a plane figure with following properties. From the Greek poly = many and gon = angle 1. A closed figure formed by 3 or more line segments called Sides 2. The sides intersect at points called the vertices. 3. The angle between two sides is called an interior angle or vertex angle. 4. You name a polygon by listing its vertices consecutively.

3. Describing Polygons These are Not Polygons These are Polygons

4. # of SidesPolygon Name# of SidesPolygon Name 3Triangle10Decagon 4Quadrilateral11Hendecagon 5Pentagon12Dodecagon 6Hexagon1313-gon 7Heptagon1414-gon 8Octagon1515-gon 9Nonagonnn-gon Describing Polygons Polygons are named by the number of Sides

5. Describing Polygons Convex Concave Rubber Band Test: If you can wrap a rubber band around the polygon, and it touches all parts of every side, then it is convex. Polygon is Convex if for any two points inside polygon, the line segment joining these two points is also inside. A figure not convex is Concave.

6. The following figures are convex. Describing Polygons

7. The following figures are concave. Note the red line segment drawn between two points inside the figure that also passes outside of the figure. Describing Polygons

8. Interior Angles of Quadrilaterals Regular Polygons If all sides of a polygon have equal lengths and if all angles have the same measure then the polygon is called a Regular Polygon. A regular triangle is called an Equilateral Triangle. A regular quadrilateral is called a Square. Equilateral Triangle Square Regular Pentagon Regular Hexagon Regular Octagon Some common regular polygons.

9. Some different types of REGULAR POLYGONS. These shapes are defined as a convex polygon with all sides congruent and all angles congruent

10. Describing Polygons Quadrilateral: A four-sided polygon.

11. Interior Angles of Quadrilaterals Diagonal The line segment connecting two nonadjacent vertices in a polygon. are all diagonals

12. Interior Angles of Quadrilaterals So, what could you conclude about the total degree measure inside the quadrilateral? Could you say this about any quadrilateral? A quadrilateral has 4 sides. If we draw a line segment connecting 2 of its opposite vertices, we'll have 2 triangles.

13. Interior Angles of Quadrilaterals Theorem 6.1 Interior Angles of a Quadrilateral The sum of the measures of the interior angles of a Quadrilateral is 360°. m  A + m  B + m  C + m  D = 360°

14. Describing Polygons Number of sidesType of PolygonSum of interior angles 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Hetagon 8Octagon 9Nonagon 10Decagon 11Hendecagon 12Dodecagon 100Hectagon

15. Describing Polygons Convex Polygon# of Sides# of TrianglesSum of Angles Triangle31180 x 1 = 180 Quadrilateral42 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 n The Angle Sum of a Convex Polygon: n-gon

16. Interior Angles of Quadrilaterals Find m  B, m  C, and m  D Example 1 x° 55° B C D A

17. Interior Angles of Quadrilaterals Find m  B, m  C, and m  D. Is quadrilateral ABCD regular? Example 2 (x - 20)° x° 80° B C D A

18. Describing Polygons

19. Homework: pp. 325 – 328 12 – 20 even 24 – 38 even, 42 – 52 even