This parallelogram is a rhomboid as its angles are oblique.
|Edges and vertices||4|
|Symmetry group||C2 (2)|
In geometry, a parallelogram is a quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length, and the opposite angles of a parallelogram are equal. The three-dimensional counterpart of a parallelogram is a parallelepiped.
The etymology (in Greek παραλληλ-όγραμμον, a shape "of parallel lines") reflects the definition.
(since these are angles that a transversal makes with parallel lines AB and DC ).
Also, side AB is equal in length to side DC, since opposite sides of a parallelogram are equal in length.
Therefore triangles ABE and CDE are congruent (ASA postulate, two corresponding angles and the included side).
Since the diagonals AC and BD divide each other into segments of equal length, the diagonals bisect each other.
Separately, since the diagonals AC and BD bisect each other at point E, point E is the midpoint of each diagonal.
The area formula,
can be derived as follows:
The area of the parallelogram to the right (the blue area) is the total area of the rectangle less the area of the two orange triangles. The area of the rectangle is
and the area of a single orange triangle is
Therefore, the area of the parallelogram is
Let and let denote the matrix with columns a and b. Then the area of the parallelogram generated by a and b is equal to | det(V) |
Let and let Then the area of the parallelogram generated by a and b is equal to
Let . Then the area of the parallelogram with vertices at a, b and c is equivalent to the absolute value of the determinant of a matrix built using a, b and c as rows with the last column padded using ones as follows:
[[File:|right|250px]] A parallelogram is a polygon with four sides. It has two pairs of parallel sides (sides which never meet) and four edges. The opposite sides of a parallelogram have the same length (they are equally long). The word "parallelogram" comes from the Greek word "parallelogrammon" (bounded by parallel lines). Rectangles, rhombuses, and squares are all parallelograms.
As shown in the picture on the right, because triangles ABE and CDE are congruent (have the same shape and size),
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