![]() ![]() Square – A parallelogram with four sides of equal length and angles of equal size (right angles).Ī simple (non-self-intersecting) quadrilateral is a parallelogram if and only if any one of the following statements is true:. ![]() Any parallelogram that is neither a rectangle nor a rhombus was traditionally called a rhomboid but this term is not used in modern mathematics. Rhombus – A parallelogram with four sides of equal length.Rectangle – A parallelogram with four angles of equal size (right angles).The etymology (in Greek παραλληλ-όγραμμον, parallēl-ógrammon, a shape "of parallel lines") reflects the definition. The three-dimensional counterpart of a parallelogram is a parallelepiped. 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.īy comparison, a quadrilateral with at least one pair of parallel sides is a trapezoid in American English or a trapezium in British English. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure. In Euclidean geometry, a parallelogram is a simple (non- self-intersecting) quadrilateral with two pairs of parallel sides. This parallelogram is a rhomboid as it has no right angles and unequal sides.Īb sin θ (product of adjacent sides and sine of the vertex angle determined by them)
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