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Parallelogram
A quadrilateral with both pairs of opposite sides parallel and equal in length.
Try this Drag the orange dots on each vertex
to reshape the parallelogram. Notice how the opposite sides remain the same length and parallel.
(If there is no image below, see support page.)
A parallelogram is a
quadrilateral with opposite sides
parallel and
congruent. It is the "parent" of some other quadrilaterals,
which are obtained by adding restrictions of various kinds:
- A rectangle is a parallelogram but with all angles fixed at 90°
- A rhombus is a parallelogram but with all sides equal in length
- A square is a parallelogram but with all sides equal in length and all angles fixed at 90°
Properties of a parallelogram
| Base |
Any side can be considered a base. Choose any one you like. If used to calculate the area (see below) the corresponding altitude must be used.
In the figure above, one of the four possible bases and its corresponding altitude has been chosen. |
| Altitude (height) |
The altitude (or height) of a parallelogram is the perpendicular distance
from the base to the opposite side (which may have to be extended). In the figure above, the altitude corresponding to the base CD is shown. |
| Area |
The area of a parallelogram can be found by multiplying a base by the corresponding altitude. See also Area of a Parallelogram |
| Perimeter |
The distance around the parallelogram. The sum of its sides. See also Perimeter of a Parallelogram |
Parallelogram Facts
These facts are true for parallelograms and the descendant shapes: square, rectangle and rhombus.
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The diagonals bisect each other
Each diagonal cuts the other diagonal into two equal parts. In the figure on the right,
drag any vertex and see that this is always true.
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Opposite angles are equal
In the figure on the right notice that as you drag any vertex, the opposite angles are always equal.
For example ∠CAB = ∠BDC.
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Consecutive angles are supplementary
As you drag any vertex in the figure on the right, you can see that consecutive angles are always supplementary (add to 180°)
For example ∠ABD + ∠BDC =180°. This is a result of the line
BD  AB CD |
Related polygon topics
General
Types of polygon
Area of various polygon types
Perimeter of various polygon types
Angles associated with polygons
Named polygons
(C) 2007 Copyright John Page
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