a quadrilateral ABCD possessing a point P in its plane such that the four triangles ABP, BCP, CDP, and DAP are all congruent.a quadrilateral in which each diagonal bisects two opposite interior angles.a quadrilateral in which the diagonals are perpendicular and bisect each other.a quadrilateral with four sides of equal length (by definition).a parallelogram in which the diagonals are perpendicular (an orthodiagonal parallelogram).a parallelogram in which at least two consecutive sides are equal in length.a parallelogram in which a diagonal bisects an interior angle.The surface we refer to as rhombus today is a cross section of the bicone on a plane through the apexes of the two cones.Ī simple (non- self-intersecting) quadrilateral is a rhombus if and only if it is any one of the following: The word "rhombus" comes from Ancient Greek: ῥόμβος, romanized: rhombos, meaning something that spins, which derives from the verb ῥέμβω, romanized: rhémbō, meaning "to turn round and round." The word was used both by Euclid and Archimedes, who used the term "solid rhombus" for a bicone, two right circular cones sharing a common base. The rhombus is often called a " diamond", after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to a rhombus with a 60° angle (which some authors call a calisson after the French sweet – also see Polyiamond), and the latter sometimes refers specifically to a rhombus with a 45° angle.Įvery rhombus is simple (non-self-intersecting), and is a special case of a parallelogram and a kite. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. In plane Euclidean geometry, a rhombus (plural rhombi or rhombuses) is a quadrilateral whose four sides all have the same length. The rhombus has a square as a special case, and is a special case of a kite and parallelogram.
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