A parallelogram is a two-dimensional rhomboid or quadrilateral with four sides. The four sides, or edges, consist of two pairs, each with the opposite side parallel and congruent. The two pairs of consecutive angles, or vertices, in a parallelogram are supplementary, which means that the sum of the angles in each consecutive pair is 180 degrees.
The perimeter of a parallelogram is obtained through the formula 2(a + b), in which "a" and "b" represent the lengths of the opposite and congruent sides. The area of a parallelogram is determined by multiplying the length of its base by its height, the same formula which is used for a finding the area of a rectangle. This is because a parallelogram can be rearranged into a rectangle by dividing it into a right triangle and a trapezoid and then moving the right triangle over to the other side.
Most of the theorems governing parallelograms are from Euclidean geometry and date back to more than 2,000 years ago. Euclid of Alexandria's major work, "Elements," contains the text of what was used as the standard basis of first-year geometry. Euclid's geometry theorems serve as fundamental exercises in mathematical deduction and were studied by individuals such as Abraham Lincoln as a means of heightening their overall powers of reasoning.