Definition:Quadrilateral/Parallelogram
Definition
A parallelogram is a quadrilateral whose opposite sides are parallel to each other, and whose sides may or may not all be the same length.
Base
In a given parallelogram, one of the sides is distinguished as being the base.
It is immaterial which is so chosen, but usual practice is that it is one of the two longer sides.
In the parallelogram above, line $AB$ is considered to be the base.
Altitude
An altitude of a parallelogram is a line drawn perpendicular to its base, through one of its vertices to the side opposite to the base (which is extended if necessary).
In the parallelogram above, line $DE$ is an altitude of the parallelogram $ABCD$.
The term is also used for the length of such a line.
Also see
- Rectangle is Parallelogram: a rectangle is a parallelogram all of whose angles are equal to a right angle.
- Altitude of Rectangle: the altitude of a rectangle is equal to one of its sides which is adjacent to its base.
- Results about parallelograms can be found here.
Euclid's Definitions
In the words of Euclid:
- Of quadrilateral figures, a square is that which is both equilateral and right-angled; an oblong that which is right-angled but not equilateral; a rhombus that which is equilateral but not right-angled; and a rhomboid that which has its opposite sides equal to one another but is neither equilateral nor right-angled. And let quadrilaterals other than these be called trapezia.
(The Elements: Book $\text{I}$: Definition $22$)
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- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): parallelogram
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): parallelogram
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): parallelogram
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): parallelogram