3-4 The Polygon Angle-Sum TheoremM11.B.2 2.3.11.B

Objectives:1)To classify polygons

2) To find the sum of the measures of the interior and exterior angles

A Polygon is a closed plane figure with at least three sides. The sides intersect only at their endpoints, and no adjacent sides are collinear.

A. B. C.

Vocab

Identify the vertices Identify the sides Identify the angle

To name a polygon, startwith any vertex and list thevertices consecutively.

Examples: Naming a Polygon

COPY the blue table from page 144 into your notebooks.

Classify a Polygon - Sides

A convex polygon has no diagonal with points outside the polygon.

Classify a Polygon - Shape

A concave polygon has at least one diagonal with points outside the polygon.

Classify a Polygon - Shape

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

Example: Classify the Polygon

The sum of the measures of the angles of an n-gon is:

Sum = (n-2)180n = number of sides

PROOF - Triangle

Polygon Angle-Sum Theorem

A.

B. The sum of a decagon

Example: Find the Polygon Angle Sum

Find m<A in pentagon ABCDE

Example: Use the Polygon Angle-Sum Theorem

The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

Polygon Exterior Angle-Sum Theorem

Equilateral Polygon – all sides congruent. Equiangular Polygon – all angles congruent Regular Polygon – both equilateral and

equiangular.

Vocab

Find the measure of an interior angle and an exterior angle of each REGULAR polygon.

Example: Exterior Measures