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Lesson 1-6: Polygons 1
Lesson 1-6
Polygons
Lesson 1-6: Polygons 2
These figures are not polygons These figures are polygons
Definition: A closed figure formed by a finite number of coplanar segments so that each segment intersects exactly two others, but only at their endpoints.
Polygons
Lesson 1-6: Polygons 3
Classifications of a Polygon
Convex: No line containing a side of the polygon contains a point in its interior
Concave:
A polygon for which there is a line containing a side of the polygon and a point in the interior of the polygon.
Lesson 1-6: Polygons 4
Regular: A convex polygon in which all interior angles have the same measure and all sides are the same length
Irregular: Two sides (or two interior angles) are not congruent.
Classifications of a Polygon
Lesson 1-6: Polygons 5
Polygon Names
3 sides Triangle
4 sides
5 sides
6 sides
7 sides
8 sides
Nonagon
Octagon
Heptagon
Hexagon
Pentagon
Quadrilateral
10 sides
9 sides
12 sides
Decagon
Dodecagonn sides n-gon
Lesson 1-6: Polygons 6
Convex Polygon Formulas…..
2 180n
n
2 180n
360
Diagonals of a Polygon:
For a convex polygon with n sides:
The sum of the interior angles is
A segment connecting nonconsecutive vertices of a polygon
The measure of one interior angle is
The sum of the exterior angles is
The measure of one exterior angle is 360
n
Lesson 1-6: Polygons 7
Examples…..
360 36045
8n
2 180 (30 2) 180 28 180168
30 30
n
n
1. Sum of the measures of the interior angles of a 11-gon is
(n – 2)180° (11 – 2)180 ° 1620
2. The measure of an exterior angle of a regular octagon is
3. The number of sides of regular polygon with exterior angle 72 ° is
4. The measure of an interior angle of a regular polygon with 30 sides
360 3605
72n n
exterior angle