to Unit 4 Properties of Quadrilaterals Please make a new notebook. Chapter 6 Polygons and Quadrilaterals

But first … Let’s define ‘polygon’ The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means angles What else do you know about a polygon? In this activity, we are going explore the interior and exterior angle measures of polygons.

Let’s define ‘polygon’ The word ‘polygon’ is a Greek word. Poly gon Poly means many and gon means angles What else do you know about a polygon? ♥ A two dimensional object ♥ A closed figure ♥ Made up of three or more straight line segments ♥ There are exactly two endpoints that meet at a vertex ♥ The sides do not cross each other

Convex polygons have interior angles less than 180 ◦ conve x concave Concave polygons have at least one interior angle greater than 180 ◦

K1 L1 M1 N1 O1 P1 Q1 R1 S1 T1 V1 U1 Let’s practice: Decide if the figure is a polygon. If so, tell if it’s convex or concave. If it’s not, tell why not.

Ok, now where were we? Oh, yes, something about the interior and exterior angle measures ofpolygons...

Quadrilateral Pentagon 180 o 2 x 180 o = 360 o 3 4 sides 5 sides 3 x 180 o = 540 o Hexagon 6 sides 180 o 4 x 180 o = 720 o 4 Heptagon/Septagon 7 sides 180 o 5 x 180 o = 900 o diagonal 2 diagonals 3 diagonals 4 diagonals Polygons

Number of sides of the polygon Sum of the interior angle measures Can you find the pattern? Can you create an equation for the pattern? Put this table in your notes:

Behold… total sum of the interior angles of a polygon (The number of sides of a polygon – 2)(180) (n – 2)(180) = = Or, as we mathematicians prefer to say…

Number of sides of the polygon Sum of the interior angle measures Sum of the exterior angle measures 360

TADA! You have just proven two very important theorems: Polygon Angle-Sum Theorem (n-2) 180 Polygon Exterior Angle-Sum Theorem Polygon Exterior Angle-Sum Theorem Always = 360 ◦

A quick polygon naming lesson: # of sidesName 3Triangle 4Quadrilateral 5Pentagon 6Hexagon 7Heptagon/Septagon 8Octagon 9Nonagon 10Decagon 12Dodecagon nn-gon I ♥ Julius and Augustus

Look at these polygons… What is your conjecture regarding the relationship between an adjacent interior/ exterior angle pair?

A regular polygon is equilateral and equiangular Triangle Square Heptagon OctagonNonagon Pentagon Hexagon Dodecagon

Let’s practice: 1.How would you find the total interior angle sum in a convex polygon? 2.How would you find the total exterior angle sum in a convex polygon? 3.What is the sum of the interior angle measures of an 11-gon? 4.What is the sum of the measure of the exterior angles of a 15-gon? 5.Find the measure of an interior angle and an exterior angle of a hexa- dexa-super-double-triple-gon. 6.Find the measure of an exterior angle of a pentagon. 7.The sum of the interior angle measures of a polygon with n sides is Find n. (n-2)(180) The total exterior angle sum is always 360 ◦ 1620 ◦ 360 ◦ 180 ◦ 360/5 = 72 ◦ 2880 = (n-2)(180) n = 18 sides

Assignment 6-1 Practice Worksheet