1. Section 6.1 Polygons OBJECTIVES:  To identify, name, and describe polygons To find the sum of the measures of the interior and exterior angles of a polygon BIG IDEA:Measurement ESSENTIAL UNDERSTANDING: The sum of the angle measures of a polygon depends on the number of sides the polygon has. MATHEMATICAL PRACTICE: Construct viable arguments and critique the reasoning of others

2. Polygons Polygon:a ____________ figure that meets the following conditions: 1.It is formed by ____________ or more segments called ____________, such that no ____________ sides with a common endpoint are ____________. 2.Each side _______________ exactly two other ____________, one at each _______________. Vertex of a polygon:each _______________ of a ____________ of a polygon. Plural is _______________

3. EX 1: State whether the figure is a polygon. If it is, name it, and if it is not, explain why. FIGURE A:FIGURE B: C A B D B A E FIGURE C:FIGURE D: C B A E D H B E G F C D

4. Polygons are named by the number of sides they have Number of SidesType of Polygon 3 4 5 6 7 8 9 10 11 12 N

5. Properties of Polygons Convex polygon:a polygon such that ________ line containing a ____________ of the polygon contains a _____________ in the ____________ of the polygon. A polygon that is not convex is ____________ or ____________. Diagonal of a polygon:a _______________ that joins two ____________________ vertices of a polygon.

6. EX 2: State whether the polygon is convex or concave and name it based on its sides. a) b) c)

7. Polygon Angle-Sum Polygon Angle-Sum Theorem: ◦The __________ of the measures of the _____________ angles of a n-gon is __________________ Corollary to the Polygon Angle-Sum Thm: ◦The measure of each interior angle of a _____________ n-gon is _______________________ Polygon Exterior Angle-Sum Theorem: ◦The __________ of the measures of the _____________ angles of a polygon, one at each _______________ is _______________

8. Describing polygons Equiangular polygon:a polygon with ________ of its ____________ angles ______________ Equilateral polygon:a polygon with ________ of its ____________ _______________ Regular polygon:a polygon that is both __________________ and __________________

9. EX 3:Tell whether the polygon is best described as equiangular, equilateral, regular, or none of these. a) b) c)

10. Interior Angles of a Quadrilateral Interior Angles of a Quadrilateral Theorem: ◦The ____________ of the measures of the ____________ angles of a _______________ is __________ ◦The rest of this chapter will focus on polygons with four sides, or quadrilaterals.

11. EX 4: Use the information in the diagram to solve for x. a)

12. EX 5: Find the measure of each angle, then is the quadrilateral regular? b) M L J K

13. EX 6: What is the measure of an exterior angle of a regular hexagon? c)

14. 6.1 p. 325 12 – 20 all, 24 – 30 evens, 38 – 50 evens, 52 a,b 22 questions