Parallelogram

A parallelogram is a four-sided plane figure that has two sets of opposite parallel sides. Every parallelogram is a polygon Polygon

A polygon is a closed [i] planar [i] path composed of a finite number of sequential ... 

, and more specifically a quadrilateral Quadrilateral

In geometry [i], a quadrilateral is a polygon [i] with four sides and four vertices. ... 

. Special cases of a parallelogram are the rhombus Rhombus

In geometry [i], a rhombus is a quadrilateral [i] in which all of the sides are of equal length, i.e., i ... 

, in which all four sides are of equal length, the rectangle Rectangle

In geometry [i], a rectangle is defined as a quadrilateral [i] where all four of its angles are right angle [i] ... 

, in which the two sets of opposing, parallel sides are perpendicular Perpendicular

In geometry [i], two lines [i] are considered perpendicular if one falls on the other in such a way ... 

 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.

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Encyclopedia

A parallelogram is a four-sided plane figure that has two sets of opposite parallel sides. Every parallelogram is a polygon Polygon

A polygon is a closed [i] planar [i] path composed of a finite number of sequential ... 

, and more specifically a quadrilateral Quadrilateral

In geometry [i], a quadrilateral is a polygon [i] with four sides and four vertices. ... 

. Special cases of a parallelogram are the rhombus Rhombus

In geometry [i], a rhombus is a quadrilateral [i] in which all of the sides are of equal length, i.e., i ... 

, in which all four sides are of equal length, the rectangle Rectangle

In geometry [i], a rectangle is defined as a quadrilateral [i] where all four of its angles are right angle [i] ... 

, in which the two sets of opposing, parallel sides are perpendicular Perpendicular

In geometry [i], two lines [i] are considered perpendicular if one falls on the other in such a way ... 

 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 Tessellation

A tessellation or tiling of the plane [i] is a collection of plane figure [i]s that fills th ... 

 with any parallelogram.

The three-dimension Dimension

In common usage, a dimension is a parameter [i] or measurement [i] required to define the characteristi ... 

al counterpart of a parallelogram is a parallelepiped Parallelepiped

In geometry [i], a parallelepiped or parallelopipedon is a three-dimensional figure like a cube [i] ... 

.

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 Cross product

In mathematics [i], the cross product is a binary operation [i] on vector [i]s in a three-dimensi ... 

 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

• Parallelogram of force
• Fundamental parallelogram Fundamental pair of periods
  
  In mathematics [i], a fundamental pair of periods is an ordered pair [i] of complex number [i]s that def ... 
  
  
• Synthetic geometry
  

External links

• 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"
• with animated applet
• interactive applet
• 
  

Categories:

• Quadrilaterals