Paralelkenarls

Paralelkenarls, known in English as parallelograms, are quadrilaterals with both pairs of opposite sides parallel. This arrangement implies that opposite sides are equal in length and opposite angles are equal, giving a stable, slanted shape often described as a “leaning” rectangle or a rhombus that can slide along its base.

Key properties include that the diagonals bisect each other, intersecting at a common midpoint. The sum of the interior angles in a parallelogram is always 360 degrees. The area can be computed as base times height, or as the product of the lengths of two adjacent sides times the sine of the included angle. The area is also equal to one half the product of the diagonals multiplied by the sine of the angle between them.

Perimeter is 2(a + b), where a and b are the lengths of adjacent sides. Special cases are common: rectangles are parallelograms with all angles equal to 90 degrees; rhombuses have all sides equal in length and diagonals that are perpendicular; squares are both rectangles and rhombuses, with all sides equal and all angles right angles.

In vector form, a parallelogram can be described by two adjacent side vectors a and b. The area is |a| |b| sin φ, where φ is the angle between the vectors. Parallelograms are foundational in geometry and appear in various applications, including architecture, computer graphics, and the study of vector addition.

Term notes: The English term is parallelogram; in Turkish, paralelkenar refers to this shape, with paralelkenarlar as the plural.