User talk:Rapcsatlanta82
R.A.P.C.S (Richard Allen Prepatory Charter School) Is presenting you a Parallelogram Project. This Page will show you what is a Parallelogram and what does it do. We will show you the three main things about an Parallelogram.
Parallelogram
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. 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 three-dimensional counterpart of a parallelogram is a parallelepiped.
Properties Opposite sides of a parallelogram are equal in length. Opposite angles of a parallelogram are equal in measure. Adjacent angles are supplementary (add up to 180 degrees). The area, A, of a parallelogram is A = bh, where b is the base of the parallelogram and h is its height. Opposite sides of a parallelogram are parallel (by definition) and so will never intersect. The area of a parallelogram is twice the area of a triangle created by one of its diagonals. Any line through the midpoint of a parallelogram bisects the area. The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides. The diagonals of a parallelogram bisect each other. Any non-degenerate affine transformation takes a parallelogram to another parallelogram. There is an infinite number of affine transformations which take any given parallelogram to a square. 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 a rectangle. The perimeter of a parallelogram is 2(a + b) where a and b are the lengths of adjacent sides. The sum of the squares of the sides equals the sum of the squares of the diagonals.
Types of parallelogram Rhomboid - A quadrilateral whose opposite sides are parallel and adjacent sides are unequal, and whose angles are not right angles Rectangle - A parallelogram with four angles of equal size (right angles). Rhombus - A parallelogram with four sides of equal length. Square - A parallelogram with four sides of equal length and four angles of equal size (right angles).
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