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The definition is that opposite sides are parallel. That doesn't tell is they are same length or not. Should a parallelogram be of the special case of having it, then it is called rhombus, or in the case that also all angles are 90°, it's called a square.
A circle is an ellipse with an eccentricity of zero. Both foci of that ellipse are at the same point. In the special case of the circle, that point is called the "center".
A rectangle is classed as any quadrilateral with four right angles, whereas a square is classed as a rectangle with all sides the same length. This being the case, all squares can be called rectangles, not all rectangles can be called squares, as some have sides of different lengths.
"Vertical" in this case means they share the same Vertex (corner point), not the usual meaning of up-down.
a polygon with all sides the same length and all angles the same measure is called?