A Square has four equal length sides
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It has four sides of equal length and the corner angles are all equal.
It is still a rhombus if all four of its sides are of equal length.
Yes. A parallelogram has two pairs of opposite sides parallel (and each pair of equal length). A rhombus has two pairs of opposite sides parallel (and each of those pairs of opposite sides are of equal length), thus it is a parallelogram. It is a special case of parallelogram where all four sides are equal in length, not just the opposite pairs.
If it is referred to as a REGULAR pentagon, then it has equal length sides. An Asymmetric pentagon has NON-equal length sides.
A parallelogram has two sets of parallel sides. It can have four sides that are equal in length. That is why a square is also a parallelogram. You can have a parallelogram with two sets of parallel sides, all of which are equal in length, but they do not meet in right angles. It looks kind of like a lopsided or squished square, and it is called a rhombus.