Figures
and polygons
Polygon
A
polygon is a closed figure made by joining line segments, where each line
segment intersects exactly two others.
Examples: The
following are examples of polygons:
The
figure to the right is not a polygon, since it is not a closed figure:
This
figure is not a polygon, since it is not made of line segments:
This
figure is not a polygon, since its sides do not intersect in exactly two places
each:
Regular
Polygon
A
regular polygon is a polygon whose sides are all the same length, and whose
angles are all the same. The sum of the angles of a polygon with n
sides, where n is 3 or more, is 180° × (n - 2)
degrees.
Examples: The
following are examples of regular polygons:
Examples: The
following are not examples of regular polygons:
Vertex
1)
The vertex of an angle is the point where the two rays that form the angle
intersect.
2)
The vertices of a polygon are the points where its sides intersect.
Triangle
A
three-sided polygon. The sum of the angles of a triangle is 180 degrees.
Examples:
Equilateral
Triangle or Equiangular Triangle
A
triangle having all three sides of equal length. The angles of an equilateral
triangle all measure 60 
degrees.
Examples:
Isosceles
Triangle
A
triangle having two sides of equal length.
Examples
Scalene
Triangle
A
triangle having three sides of different lengths.
Examples:
Acute
Triangle
A
triangle having three acute angles. |
Examples:
Obtuse
Triangle
A
triangle having an obtuse angle. One of the angles of the triangle measures
more than 90 degrees.
Examples
Right
Triangle
A
triangle having a right angle. One of the angles of the triangle measures 90
degrees. The side opposite the right angle is called the hypotenuse. The two
sides that form the right angle are called the legs. A right triangle has the
special property that the sum of the squares of the lengths of the legs equals
the square of the length of the hypotenuse. This is known as the Pythagorean
Theorem.
Example:
For
the right triangle above, the lengths of the legs are A and B, and the
hypotenuse has length C. Using the Pythagorean Theorem, we know that A2 + B2 = C2.
Example: 
In
the right triangle above, the hypotenuse has length 5, and we see that 32 + 42 = 52
according to the Pythagorean Theorem.
Quadrilateral
A
four-sided polygon. The sum of the angles of a quadrilateral is 360
degrees.
Examples:
Rectangle
A
four-sided polygon having all right angles. The sum of the angles of a
rectangle is 360 degrees.
Examples:
Square
A
four-sided polygon having equal-length sides meeting at right angles. The sum
of the angles of a square is 360 degrees. Examples:
Parallelogram
A
four-sided polygon with two pairs of parallel sides. The sum of the angles of a
parallelogram is 360 degrees.
Examples
Rhombus
A
four-sided polygon having all four sides of equal length. The sum of the angles
of a rhombus is 
360
degrees. Examples:
Trapezoid
A
four-sided polygon having exactly one pair of parallel sides. The two sides
that are parallel are called the bases of the trapezoid. The sum of the angles
of a trapezoid is 360 degrees.
Examples:
Pentagon
A five-sided polygon. The sum of the angles of a pentagon is 540
degrees.
Examples:
|
A regular pentagon:
|
An irregular pentagon:
|
Hexagon
A six-sided polygon. The sum of the angles of a hexagon is 720
degrees.
Examples:
|
A regular hexagon:
|
An irregular hexagon:
|
Octagon
An
eight-sided polygon. The sum of the angles of an octagon is 1080 degrees.
Examples:
|
A regular octagon:
|
An irregular octagon:
|
Circle
A
circle is the collection of points in a plane that are all the same distance
from a fixed point. The fixed point is called the center. A line segment joining the center to any point on the circle is
called a radius.
Example: The blue line is the radius r, and the collection of red points
is the circle.
