Parallelogram, Quadrilateral, and Rectangles
First off both of these images are parallelogram because the arrows show that both the rectangle and the square (diamond/whatever you want to call it) have pairs of parallel sides so we know that both these shapes are parallelograms
Secondly, these shapes are both quadrilaterals. A quadrilateral, by definition, is simply a four-sided figure. Both a rectangle and a square are four-sided figures so these are both quadrilaterals.
Lastly, these figures are both rectangles. Yes I know one is a square and one is a rectangle but a square is a special four sided figure that can classify as a rectangle. Every square is a rectangle but not every rectangle is a square. A rectangle by definition is a four sided polygon with two pairs of parallel sides, congruent sides, and four 90 degree interior angles.
Hope this helped :)
