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Why is a rhombus special?
A rhombus is a special case of a parallelogram where all side are the same length.
How is a rhombus the same as a parallelogram?
A rhombus is a parallelogram, but a parallelogram isn't always a rhombus. A rhombus is a parallelogram where all the lines are the same length.
Are all the side of a parallelogram the same?
no
What is a parallelogram that is not a square with all the sides the same length?
A rhombus
How can you convince me that a rhombus is a parallelogram but a parallelogram is not a rhombus?
A parallelogram requires that opposite sides are parallel and of the same length; it is not a requirement that all four sides are of the same length. A rhombus requires that opposite sides are parallel and all four sides are of the same length. It is possible that a parallelogram can have all four sides of the same length; when it does it now fulfils the requirements of a rhombus, and so is a rhombus. Thus a rhombus is a type of parallelogram (all rhombuses are parallelograms), but there are parallelograms which are not rhombuses (those where there are two sides of one length (opposite and parallel) and the other two sides of a different length).
