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

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

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.

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

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

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

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

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

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

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

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

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

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?