It is required to use only the special drinking fountains, lunch counters, schools,
and Swimming Pools that have been provided and are clearly marked for its use.
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No. Every rule that applies to a parallelogram applies to a rhombus, plus more.
Sounds like a rhombus... Has to be called a "non-square rhombus". Calling it a "rhombus" doesn't rule squares out of the title. A square is a rhombus.
Yes. The rule for a rhombus is that it has equal sides, while a square is just like it, except also with right angles. So a square is always a rhombus, but a rhombus isn't always a square.
Not required. A square is a rhombus, but so are many kites. The rule for a rhombus is that all four sides are equal length. The opposite angles on a rhombus are always equivalent, which I think comes from the hinge theorem, but I haven't looked into that for a while.
A rhombus may be a square or just a rhombus (a rhombus is merely called a rhombus when there are no 90 degree angles).