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# Chapter 6: Polygons and Quadrilaterals - PowerPoint PPT Presentation

Chapter 6: Polygons and Quadrilaterals. Polygon terms we know:. Polygons. Descriptors or parts. Quadrilateral. Pentagon. Concave. Trapezoid. Convex. Hexagon. Kite. Octogon. Rectangle. Vertex. Side. Square. Diagonal. Regular Polygon. The Polygon Angle-Sum Theorems. Objective:

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Presentation Transcript

Polygon terms we know:

Polygons

Descriptors or parts

Pentagon

Concave

Trapezoid

Convex

Hexagon

Kite

Octogon

Rectangle

Vertex

Side

Square

Diagonal

Regular Polygon

### The Polygon Angle-Sum Theorems

Objective:

To find the sum of the measures of the interior angles of a polygon

To find the sum of the measures of the exterior angles of a polygon

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

Polygon Sum Theorem

1800 (n – 2)

Example:

Rectangle – 4 interior angles

4 right angles

4 (900) = 3600

nth term:

1800 (n – 2)

The sum of the measures of a quadrilateral is 3600

n = 4

1800 (4 -2)= 3600

a + b + c = 1800

x + y + z = 1800

x

a

Triangle Sum Conjecture

y

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

b