Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside...

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Polygon Basics

Transcript of Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside...

Page 1: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

Polygon Basics

Page 2: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 3: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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

Page 4: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 5: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 6: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

Triangle:  A polygon with three sides.

Triangles are named by using letters at their vertices:

Page 7: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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).

Page 8: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 9: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 10: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 11: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 12: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 13: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 14: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 15: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 16: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 17: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

Rhombus:  A parallelogram with four equal sides.

Page 18: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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.

Page 19: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

Rectangle:  A parallelogram with four right angles.

Page 20: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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

Page 21: Polygon Basics. Polygons can be concave or convex. Concave: If, when you join any two points inside a figure, the resulting line segment goes outside.

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