In Euclidean geometry, a rhombus, plural rhombi or rhombuses, is a simple quadrilateral whose four sides all have equal length. Another name is equilateral quadrilateral, since equilateral means that all of its sides are the same in length. The rhombus is frequently called a diamond, after the diamonds suit in the playing cards, or a lozenge, though the former sometimes is in reference specifically to a rhombus with a 60 degree angle, and the latter occasionally is in reference specifically to a rhombus with a 45 degree angle.
Every rhombus is a parallelogram, and a rhombus with right angles is called a square.
The word rhombus comes from Greek rhombos, meaning something that spins, which comes from the verb rhembo, meaning “to turn round and round”. The word was utilized both by Euclid and Archimedes, who used the term “solid rhombus” for two right circular cones sharing a common base.
Every rhombus has two diagonals connecting pairs of opposite corners, and two pairs of parallel edges. Utilizing congruent triangles, one can prove that the rhombus is symmetric across each of the diagonals.
Not every parallelogram is a rhombus, though any parallelogram with perpendicular diagonals is a rhombus. In general, any quadrilateral with perpendicular diagonals, one of which is a line of symmetry, is a kite. Every rhombus is a kite, and any quadrilateral that is both a parallelogram and a kite is a rhombus.
Image Caption: Rhombus. Credit: Wikipedia