Explanation:
Parallelogram

This parallelogram is a rhomboid as its angles are oblique.

Type

quadrilateral

Edges and Vertices

4

Area

B × H;
ab sin θ

Properties

convex

In geometry, a parallelogram is a quadrilateral with two pairs of parallel sides. In Euclidean Geometry,
the opposite or facing sides of a parallelogram are of equal length and the
opposite angles of a parallelogram are of equal measure. (Our solved example in mathguru.com uses this concept)
The congruence
of opposite sides and opposite angles is a direct consequence of the Euclidean
Parallel Postulate and neither condition can be proven without appealing to the
Euclidean Parallel Postulate or one of its equivalent formulations. The
threedimensional counterpart of a parallelogram is a parallelepiped.
Properties
1. Opposite
sides of a parallelogram are parallel (by definition) and so will never
intersect.
2. Opposite
sides of a parallelogram are equal in length. (congruent)
3. Opposite
angles of a parallelogram are equal in measure.
4.
Adjacent
angles are supplementary (add up to 180 degrees). (Our solved example in
mathguru.com uses this concept)
5. The
area of a parallelogram is twice the area of a triangle created by one of its
diagonals.
6. The
area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.
7. The diagonals of a parallelogram bisect each other.
8. Any
line through the midpoint of a parallelogram bisects the area.
9. Any
nondegenerate affine
transformation takes a
parallelogram to another parallelogram.
There is an infinite number of affine transformations which take any given
parallelogram to a square.
10. A
parallelogram has rotational
symmetry of order 2 (through
180°). If it also has two lines of reflectional
symmetry then it must be a rhombus
or an oblong.
11. The
perimeter of a parallelogram is 2(a + b) where a and b are the lengths of adjacent sides.
12. The sum
of the squares of the sides equals the sum of the squares of the diagonals. This is the parallelogram law.
http://en.wikipedia.org/wiki/Parallelogram
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