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parallelogram (Definition)

A parallelogram is a quadrilateral whose opposite sides are parallel.

Some special parallelograms have their own names: squares, rectangles, rhombuses. A rectangle is a parallelogram whose all angles are equal (i.e. $ 90^\circ$), a rhombus is a parallelogram whose all sides are equal, and a square is a parallelogram that is a rectangle and a rhombus at the same time.

\includegraphics{parallelograms}

Every parallelogram have their opposite sides and opposite angles equal. Also, adjacent angles of a parallelogram always add up to $ 180^\circ$, and the diagonals bisect each other.

A base of a parallelogram is one of its sides. Any side of a parallelogram can be selected as its base. Once a base has been selected, the height of the parallelogram is defined to be the length of any line segment perpendicular to the base which extends from the base to the opposite side parallel to the base. The area of a parallelogram with base length $ b$ and height $ h$ is given by the formula $ A = \frac{1}{2}bh$.

There is also a neat relation between the length of the sides and the lengths of the diagonals called the parallelogram law.



"parallelogram" is owned by drini. [ full author list (3) | owner history (1) ]
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See Also: parallelogram theorems, quadrilateral, rectangle, rhombus, square, parallelogram law, kite, rhomboid, proof of parallelogram theorems, parallelotope


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compass and straightedge construction of parallel line (Algorithm) by pahio
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Cross-references: parallelogram law, relation, area, perpendicular, line segment, length, diagonals, adjacent, opposite, sides, rhombus, angles, rhombuses, rectangles, squares, parallel, opposite sides, quadrilateral
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This is version 6 of parallelogram, born on 2001-12-11, modified 2007-06-18.
Object id is 1081, canonical name is Parallelogram.
Accessed 18321 times total.

Classification:
AMS MSC51-00 (Geometry :: General reference works )

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