Chapter 6:Chapter 6:Polygons and Polygons and QuadrilateralsQuadrilaterals

Polygon terms we know:

Kite

Trapezoid

Polygons

Quadrilateral

Rectangle

Square

ConcaveConvex

SideVertex

Diagonal Regular Polygon

Descriptors or parts

HexagonPentagon

Octogon

6-16-1The Polygon Angle-Sum The Polygon Angle-Sum

TheoremsTheorems

Objective:Objective:•To find the sum of the measures To find the sum of the measures of the interior angles of a polygonof the interior angles of a polygon•To find the sum of the measures To find the sum of the measures of the exterior angles of a polygonof the exterior angles of a polygon

Theorem 6-1The sum of the measures of the n interior angles of an n-gon is ______________.

Polygon Sum Theorem

1800 (n – 2)

nth term: 1800 (n – 2)

1800 (4 -2)= 3600

Rectangle – 4 interior angles

4 right angles

4 (900) = 3600

Example:

n = 4

The sum of the measures of the

interior angles of a quadrilateral is 3600

Three Types of Polygons

Addition Property of equality

Triangle Sum Conjecturex

y

zc

b

a

a + b + c = 1800

x + y + z = 1800

(a + b + c) + (x + y + z) = 3600

p. 356: 7, 9, 11, 15, 17,

19, 21, 23, 25, 29, 31