What is an equilateral parallelogram often referred to when it does not have right angles?

An equilateral parallelogram is commonly known as a rhombus when it does not have right angles. A rhombus has all four sides of equal length, which aligns with the definition of an equilateral parallelogram. Additionally, the opposite angles in a rhombus are equal, and adjacent angles are supplementary.

In contrast, a rectangular parallelogram would have all right angles, which disqualifies it from being equilateral without right angles. A square is a specific type of rhombus that also includes right angles, so it does not fit the criteria described. A trapezoid, on the other hand, is a quadrilateral with only one pair of parallel sides and does not possess the properties of a parallelogram at all. Thus, the definition of an equilateral parallelogram that does not have right angles directly points to a rhombus.