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Polygons

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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

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Naming Polygons• Use capital letters• List them in consecutive order

A

E

B

C

D

Plane ABCDEPlane DEABCPlane CBAEDEtc…

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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

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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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Examples:

Tell whether each is a polygon. If a polygon, is it concave or convex?

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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

Equilateral: All sides are congruent

Equiangular: All interior angles are congruent

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Examples:

A rack for billiard balls is shaped like a regular triangle. Find the length of each side.

( 4 𝑥+2 )𝑖𝑛(6 𝑥−4 )𝑖𝑛

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Examples:Find the value of x so that the polygon is equilateral or equiangular.

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Find the value of x so that the polygon is equilateral or equiangular.

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2 3x x

2 2x x

Find the measure of each angle in this regular hexagon.