Warm Up: Investigating the Properties of Quadrilaterals

• Make a conjecture about the sum of the interior angles of quadrilaterals.

• You may use any material/equipment to help test your conjecture.

• Be prepared to justify your conclusion with the data you collect.

• You may choose to work as a group or by yourself.

Interior Angles of a Quadrilateral

The sum of the measures of the interior angles of a quadrilateral is 3600.

m1 + m2 + m3 + m4 = 3600

1

2

34

Chapter 6.1: Polygons

• Students will identify regular and

nonregular polygons.• Students will describe characteristics

of a quadrilateral.

What’s a Polygon?

A plane figure that meets the following conditions…

1. It is formed by three or more segments called sides, such that no two sides with a common endpoint are collinear.

2. Each side intersects exactly two other sides, one at each endpoint.

More Vocabulary

• Vertex (vertices): each end point of a side of a polygon

• Name vertices of a polygon consecutively.

• State whether each figure is a polygon. If not, explain why.

A B CD

E

F

• Convex polygon: a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon. Every internal angle is less than or equal to 180o.

• Concave or Nonconvex polygon: a polygon that is not convex. Always has an interior angle with a measure that is greater than 180o.

• Now draw your own example of a concave and convex polygon.

Concave Convex

• Equilateral: a polygon with all sides congruent

• Equiangular: a polygon with all of its interior angles congruent

• Regular: a polygon that is equilateral and equiangular

• Diagonal: a segment in a polygon that joins two nonconsecutive vertices.

Cool Down: Find the missing values.

1.

2.