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Which type of parallelogram has all sides equal in length?

  1. Rectangle

  2. Square

  3. Rhombus

  4. Trapezoid

The correct answer is: Rhombus

A rhombus is a type of parallelogram characterized by having all four sides equal in length. This distinct property sets it apart from other types of parallelograms. While both rectangles and squares fall under the broader category of parallelograms, they do not have the same properties concerning side lengths. A rectangle has opposite sides that are equal in length, but the adjacent sides may be different. A square, on the other hand, is a specific case of both a rectangle and a rhombus because it has all sides equal and all angles equal to 90 degrees. However, the square is more restrictive than a rhombus since it requires right angles. Trapezoids, on the other hand, do not necessarily have equal sides or parallel sides as the defining feature is having at least one pair of parallel sides, which does not apply to the idea of all four sides being equal. Therefore, the defining characteristic of a rhombus makes it the correct choice when identifying a type of parallelogram with all sides of equal length.