Name the polygons with the following number of sides:

• 3• 4• 5• 6• 7• 8• 9• 10• 12

• Triangle• Quadrilateral• Pentagon• Hexagon• Heptagon• Octagon• Nonagon• Decagon• Dodecagon

Polygons

Geometry

Mrs. King

Unit 3, Lesson 4

Definition

Polygon: a closed plane figure with at least three sides.

Video: Polygons in Architecture

Name the polygon. Then identify its vertices, sides, and

angles.

Possible names are ABCDE and EDCBA.Its vertices are A, B, C, D, and E.

Its angles are named by the vertices, A, B, C, D, and E.

Its sides are AB, BC, CD, DE, and EA.

Without the use of your notes:

Matching names with number of sides: http://www.quia.com/cm/86645.html?AP_rand=2098901149

Concentration game: http://www.quia.com/jg/1507267.html

Definition

Convex: a polygon is convex if no diagonal contains points outside the polygon.

http://img.sparknotes.com/figures/B/b333d91dce2882b2db48b8ad670cd15a/convexconcave.gif

Definition

Concave: a polygon is concave if a diagonal contains points outside the polygon.

http://img.sparknotes.com/figures/B/b333d91dce2882b2db48b8ad670cd15a/convexconcave.gif

Theorem 2-3: Polygon Interior Angle-Sum Theorem

The sum of the measures of the interior angles of an n-gon is (n - 2)180.

A decagon has 10 sides, so n = 10.

Sum = (n – 2)(180)

= (10 – 2)(180)

= 8 • 180

= 1440

Find the sum of the measures of the angles of a decagon.

Practice

• Find the sum of the measure of the interior angle of the following polygons:– 15-gon

– 20-gon

– Decagon

– Dodecagon

(n-2) x 180 video

• Cool Video!!

The figure has 4 sides, so n = 4.

Find m X in quadrilateral XYZW.

Theorem 2-4: Polygon Exterior Angle-Sum Theorem

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

http://www.mathlove.com/new3/product/img/TTA05/5.jpg

Video: General Definitions of Polygons

Definition

Equilateral polygon: a polygon with all sides congruent.

Equiangular polygon: a polygon with all angles congruent.

Regular polygon: a polygon that is both equilateral and equiangular.