Parallelogram

A quadrilateral whose opposite sides are parallel. Its opposite sides are equal in length, and its opposite angles are equal.

Quadrilateral: A polygon with four sides and four angles. A parallelogram is a quadrilateral with the additional condition that both pairs of opposite sides are parallel.
Alternate interior angles: A pair of angles formed inside two lines by a transversal, on opposite sides of that transversal. Parallel opposite sides make alternate interior angles equal, establishing equal opposite angles.
Rectangle: A quadrilateral with four right angles. It is a parallelogram whose adjacent sides meet at right angles.
Vector addition: The operation that combines vectors by adding their corresponding components. The parallelogram rule represents the sum of two vectors as the diagonal from their shared tail.
Trapezoid: A quadrilateral with at least one pair of parallel sides in the inclusive definition. Unlike a parallelogram, a trapezoid need not have both pairs of opposite sides parallel.
Parallel lines: Coplanar lines that never intersect, however far they are extended. The defining condition requires each pair of opposite sides to lie on parallel lines.
Congruent triangles: Triangles that have the same size and shape, with corresponding sides and angles equal. A diagonal divides a parallelogram into two congruent triangles, proving opposite sides are equal.
Rhombus: A quadrilateral with four equal sides. It is a parallelogram with all sides equal.
Affine transformation: A map between affine spaces that preserves points, lines, and ratios along a line. Affine maps send parallelograms to parallelograms, even when lengths and angles change.
Kite (geometry): A quadrilateral with two distinct pairs of adjacent equal sides. A kite is defined by adjacent side lengths rather than parallel opposite sides.

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