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1-29-15Unit 8

Polygons and Quadrilaterals

Polygons

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These figures are not polygons These figures are polygons

Definition: A closed figure formed by coplanar segments so that each segment intersects exactly two others, but only at their endpoints.

Polygons

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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.

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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

Diagonals of a Polygon:A segment connecting nonconsecutive vertices of a polygon

Interior angle: An angle formed by two adjacent sides inside the polygon.

Exterior angle: An angle formed by two adjacent sides outside the polygon.

Polygons

Angles of a Polygon

Interior angle

Exterior angle

Polygons

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Polygon Names3 sides Triangle4 sides5 sides6 sides7 sides8 sides

NonagonOctagonHeptagonHexagonPentagonQuadrilateral

10 sides9 sides

12 sidesDecagonDodecagonn sides n-gon

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Convex Polygon Formulas…..

2 180nn

2 180n

360

For a convex polygon with n sides:The sum of the interior angles is

The measure of one interior angle is

The sum of the exterior angles is

The measure of one exterior angle is 360n

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Examples…..

360 360 458n

2 180 (30 2) 180 28 180 16830 30

nn

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

360 360 572

n nexterior angle