Polygon Angle-Sum. A polygon is a closed plane figure with at least three sides. The sides intersect only at their endpoints and no adjacent sides are.

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Presentation transcript:

Polygon Angle-Sum

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. Yes No

To name a polygon, start at any vertex and list the others consecutively. Polygon ABCDE Polygon EDCBA Polygon DEABC

The diagonal of a polygon is a segment that connects two nonconsecutive vertices. How many diagonals can be drawn from one vertex of this shape?

A polygon is convex if no diagonal contains points outside the polygon. A polygon is concave if a diagonal contains points outside the polygon.

Polygon Name Number of Sides Triangle3 Quadrilateral4 Pentagon5 Hexagon6 Heptagon7 Octagon8 Nonagon9 Decagon10 Dodecagon12 n-gonn

Polygon Interior Angle-Sum Theorem The sum of the measures of the interior angles of an n-gon is (n-2)180.

Find the sum of the measures of the interior angles of a pentagon. Find the sum of the measures of the interior angles of a hexagon. Find the sum of the measures of the interior angles of a decagon.

Polygon Name Number of Sides 1,000,000-gon1,000,000 Sum of measures of interior angles: 179, 996, 640°

Polygon Exterior Angle-Sum Theorem The sum of the measures of the exterior angles of a polygon, one at each vertex, is 360.

Equilateral polygon - all sides are congruent Equiangular polygon – all angles are congruent Regular polygon – equilateral and equiangular

Homework Finish table and worksheet