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Are all the angles of a parallelogram can be equal in size?
They can, but usually they are not. All the angles will be equal only if your parallelogram is a rectangle.
Does a parallelogram always have four sides?
Yes, and its opposite sides are always equal and its opposite angles are always equal. The angles and the sides can be any size.
Can a parallelogram be called a rectangle square or a rhombus?
A rectangle may be called a parallelogram but they are both 4 sided quadrilaterals. A parallelogram can be called a rectangle if all four angles are right angles (90 degrees). A parallelogram can be called a rhombus if all four sides are the same size. A parallelogram can be called a square if all four angles are right angles and all four sides are the same size
A parallelogram with all sides of equal length?
Is generically called a Rhombus and specifically a Square of the 4 angles are of equal size too.
What has 2 pairs of parallel sides and 2 acute angles of the same size and 2 obtuse angles of the same size?
A parallelogram. A rhombus (a special case of parallelogram, with all 4 sides equal length) also fits this criteria.
