Parallelogram
A parallelogram is a four-sided plane figure that has two sets of opposite parallel sides. Every parallelogram is a
polygon, and more specifically a
quadrilateral. Special cases of a parallelogram are the
rhombus, in which all four sides are of equal length, the
rectangle, in which the two sets of opposing, parallel sides are
perpendicular to each other, and the square, in which all four sides are of equal length and the two sets of opposing, parallel sides are perpendicular to each other. In any parallelogram, the diagonals bisect each other, i.e, they cut each other in half.
Encyclopedia
A
parallelogram is a four-sided plane figure that has two sets of opposite parallel sides. Every parallelogram is a
polygon, and more specifically a
quadrilateral. Special cases of a parallelogram are the
rhombus, in which all four sides are of equal length, the
rectangle, in which the two sets of opposing, parallel sides are
perpendicular to each other, and the square, in which all four sides are of equal length and the two sets of opposing, parallel sides are perpendicular to each other. In any parallelogram, the diagonals bisect each other, i.e, they cut each other in half.
The parallelogram law distinguishes Hilbert spaces from other Banach spaces.
It is possible to create a
tessellation with any parallelogram.
The three-
dimensional counterpart of a parallelogram is a
parallelepiped.
The area of a parallelogram can be seen as twice the area of a triangle created by one of its diagonals. The area of a parallelogram can be found by using the formula . The area can also be computed as the magnitude of the
vector cross product of two of its non-parallel sides.
Proof that diagonals bisect each other
Prove that the diagonals of a parallelogram bisect each other.
When you look hard you can see that a parrallellograme has four sides.
Proof:
, k is an element of the real numbers
since
18:56, 25 September 2006
since E,D,B are collinear, by the division-point theorem,
k + k = 1
2k = 1
k = 0.5
sub k = 0.5 into:
also sub k = 0.5 into:
by the division-point theorem,
by adding the division ratios to the parallelogram, we see that E divides both diagonals in the ratio 1:1, and E bisects AC and BD.
Therefore, the diagonals of a parallelogram bisect each other.
See also
External links
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- at cut-the-knot
- at cut-the-knot
- by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
- Quadrilateral with four squares by Antonio Gutierrez from "Geometry Step by Step from the Land of the Incas"
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- with animated applet
- interactive applet
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