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Polygon Basics

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**Polygons can be concave or convex.**

Concave: If, when you join any two points inside a figure, the resulting line segment goes outside the figure, then the figure is concave. Also called nonconvex. Convex: If, when you join any two points inside a figure, the resulting line segment also lies inside the figure, then the figure is convex.

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The first figure is a concave irregular polygon, the second is a convex irregular polygon, and the third is a convex regular polygon. The circle is NOT a polygon because it is not made up of line segments. The last figure is NOT a polygon because it is not closed

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Regular Polygon: A polygon that is equiangular (all angles are equal) and equilateral (all sides are equal). Regular polygons that you might be familiar with are the equilateral triangle and the square. Below are examples of a few regular polygons.

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Irregular Polygon: A polygon whose interior angles are not equal and/or its sides are not equal in length. The following figures are examples to irregular polygons. Notice particularly the blue middle figure that although all sides are equal, it is not a regular pentagon since the interior angles are not the same.

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**Triangle: A polygon with three sides.**

Triangles are named by using letters at their vertices:

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**Quadrilateral: A polygon with 4 sides.**

Given the following figures, the first is a convex irregular quadrilateral and the second is a regular quadrilateral (a square).

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**Pentagon: A polygon with 5 sides.**

Given the following figures, the first is a nonregular convex pentagon and the second is a regular convex pentagon.

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**Hexagon: A polygon with 6 sides.**

In the picture the shape on the left (the red one) is a regular hexagon and the shape on the right (the blue one) is an example to an irregular hexagon.

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**Heptagon: A polygon with 7 sides.**

In the picture the shape on the left (the red one) is a regular heptagon and the shape on the right (the blue one) is an example to an irregular heptagon.

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**Octagon: A polygon with 8 sides**

Given the following figures, the first is a regular (convex) octagon and the second is an irregular, concave octagon.

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**Nonagon: A polygon with 9 sides.**

Given the figures below, the first is a concave irregular nonagon and the second is a regular (convex) nonagon.

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**Decagon: A polygon that has 10 sides**

In the picture is a regular decagon. An irregular decagon could be an arbitrary polygon with 10 sides.

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**Trapezoid: A quadrilateral that has only one pair of parallel sides.**

The parallel sides of a trapezoid are called bases. The angles that share a base as a common side are called a pair of base angles. If the sides of a trapezoid that are not parallel are exactly the same length, the trapezoid is said to be isosceles.

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**Isosceles Trapezoid: A trapezoid whose non-parallel sides are exactly the same length.**

Where have you seen that term before? Compare the base angles of an isoceles trapezoid. Now look at the diagonals of an isoceles trapezoid. Compare their lengths.

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**Parallelogram: A quadrilateral with opposite sides that are parallel.**

The figure is a parallelogram. Aside from having opposite sides that are parallel, parallelograms have several other special properties.

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**Rhombus: A parallelogram with four equal sides.**

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**Kite: A quadrilateral that is not a parallelogram, but has two pairs of equal sides.**

A kite, like a parallelogram, has two pairs of equal sides. But in a kite the equal sides are adjacent to each other.

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**Rectangle: A parallelogram with four right angles.**

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**Square: A quadrilateral that has four right angles and four equal sides.**

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What is a polygon to you?

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