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

3. 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
EX 1: State whether the figure is a polygon. If it is, name it, and if it is not, explain why.

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

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.
Properties of Polygons

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

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 _______________
Polygon Angle-Sum

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

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

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.
Interior Angles of a Quadrilateral

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

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

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