2. 6.1 POLYGONS

3. WHAT IS POLYGON? Formed by three or more segments (sides). Each side intersects exactly two other sides, one at each endpoint. Has vertex/vertices.

4. These are Not Polygons These are Polygons

5. # of SidesPolygon Name# of SidesPolygon Name 3Triangle10gon 4Quadrilateral11gon 5 12gon 6 13gon 7 14gon 8 15gon 9 n Polygons are named by the number of Sides

6. CONCAVE VS. CONVEX Convex: if no line that contains a side of the polygon contains a point in the interior of the polygon. Concave: if a polygon is not convex. interior

7. 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.

8. EXAMPLE Identify the polygon and state whether it is convex or concave. Concave polygon Convex polygon

9. A polygon is equilateral if all of its sides are congruent. A polygon is equiangular if all of its interior angles are congruent. A polygon is regular if it is equilateral and equiangular.

10. DECIDE WHETHER THE POLYGON IS REGULAR. ) ) ) ) ) )) ) )

11. A Diagonal of a polygon is a segment that joins two nonconsecutive vertices. diagonals

12. INTERIOR ANGLES OF A QUADRILATERAL THEOREM The sum of the measures of the interior angles of a quadrilateral is 360°. A B C D m<A + m<B + m<C + m<D = 360°

13. EXAMPLE Find m<Q and m<R. R x P S 2x° Q 80° 70° x + 2x + 70° + 80° = 360° 3x + 150 ° = 360 ° 3x = 210 ° x = 70 ° m< Q = x m< Q = 70 ° m<R = 2x m<R = 2(70°) m<R = 140 °

14. FIND M<A A B C D 65° 55° 123°

15. Use the information in the diagram to solve for j. 60° 150° 3j ° 60° + 150° + 3j ° + 90° = 360° 210° + 3j ° + 90° = 360° 300 ° + 3j ° = 360 ° 3j ° = 60 ° j = 20

16. Find m  B, m  C, and m  D. Is quadrilateral ABCD regular? (x - 20)° x° 80° B C D A