3 4 The Polygon Angle Sum Theorems Chapter

3. 4 The Polygon Angle-Sum Theorems Polygon: a closed plane figure with at least

Naming a Polygon Name a polygon by its vertices. A ABCDE or AEDCB B

Naming a Polygon Three polygons are pictured. Name each polygon: L P M O

Classifying a Polygon by the number of sides: Sides 3 4 5 6 7

Convex vs. Concave l A Convex Polygon has all vertices pointing “out” l A

Classify l Classify each polygon by its sides. Identify each as convex or concave:

Sum of Polygon Angle Measures Use triangles to figure out the sum of the

Sum of Polygon Angle Measures Number of Sides 3 4 5 6 n Number

Theorem 3 -9 Polygon Angle Sum Theorem The sum of the measures of the

Polygon Angle Sum The sum of the measures of the angles of a given

Using Polygon Angle-Sum Theorem Find the measure of <Y in pentagon TVYMR at the

Using Polygon Angle-Sum Theorem Pentagon ABCDE has 5 congruent angles. Find the measure of

Exterior Angles What do you notice about each set of exterior angles? 80° 75°

Theorem 3 -10 Polygon Angle. Sum Theorem The sum of one set of exterior

Polygons l l l Equilateral Polygon: all sides congruent Equiangular Polygon: all angles congruent

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3. 4 The Polygon Angle -Sum Theorems Chapter 3: Parallel and Perpendicular Lines

3. 4 The Polygon Angle-Sum Theorems Polygon: a closed plane figure with at least three sides that are segments A polygon Not a polygon; Not enclosed Not a polygon; Two sides intersect

Naming a Polygon Name a polygon by its vertices. A ABCDE or AEDCB B E D C Start at one vertex and go around in order

Naming a Polygon Three polygons are pictured. Name each polygon: L P M O N

Classifying a Polygon by the number of sides: Sides 3 4 5 6 7 8 9 10 12 n Name Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Dodecagon n-gon

Convex vs. Concave l A Convex Polygon has all vertices pointing “out” l A Concave Polygon has one or more vertices “caving in”

Classify l Classify each polygon by its sides. Identify each as convex or concave: Hexagon; Convex Octagon; Concave

Sum of Polygon Angle Measures Use triangles to figure out the sum of the angles in each polygon: # of Sides: # of Triangles: Total Degrees:

Sum of Polygon Angle Measures Number of Sides 3 4 5 6 n Number of Triangles 1 Total Degrees inside Polygon 180

Theorem 3 -9 Polygon Angle Sum Theorem The sum of the measures of the angles in a polygon is (n – 2)180. Find the sum of the measure of the angles of a 15 -gon.

Polygon Angle Sum The sum of the measures of the angles of a given polygon is 720. How many sides does the polygon have? Use (n – 2)180 :

Using Polygon Angle-Sum Theorem Find the measure of <Y in pentagon TVYMR at the right. R 135° M T Use (n – 2)180 90° Y V Write an equation to solve for <Y

Using Polygon Angle-Sum Theorem Pentagon ABCDE has 5 congruent angles. Find the measure of each angle. Use the Polygon Angle-Sum Theorem: (n – 2)180 Divide the total number of degrees by the number of angles:

Exterior Angles What do you notice about each set of exterior angles? 80° 75° 115° 2 1 150° 99° 130° 71° 70° 86° 88° 3 2: 70° 46° 1: 3:

Theorem 3 -10 Polygon Angle. Sum Theorem The sum of one set of exterior angles for any polygon is 360°. 1 5 2 4 3 m<1 + m<2 + m<3 + m<4 + m<5 = 360°

Polygons l l l Equilateral Polygon: all sides congruent Equiangular Polygon: all angles congruent Regular Polygon: all sides and all angles congruent (equiangular and equilateral) *If a polygon is a regular polygon then all of the exterior angles are also congruent.

Homework l Pg 147 1 -25, 40 -44, 47 -49