Yes and they are both 4 sided quadrilaterals
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A rhombus is quite different to a trapezoid but they are both 4 sided quadrilaterals
Both have 4 sides, 4 angles, 4 sides, and 4 vertices.
Both have 4 sides, 4 angles, 4 sides, and 4 vertices.
Not only does a rhombus always have one pair on parallel opposite sides, but it always has two! A rhombus is usually defined as a simple polygon of four sides where all the sides are the same length." If this is true of a figure then both pairs of opposite sides have to be parallel. Here is a proof for those who are interested. http://www.artofproblemsolving.com/Wiki/index.php/Rhombus#Proof_that_a_rhombus_is_a_parallelogram If there is only one pair of parallel sides in the figure, then it is a trapezoid. A rhombus is a trapezoid too.
A rectangle is not always equilateral, although it is always equiangular. A rhombus is not always equiangular, but is always equilateral. A square is both equilateral and equiangular.