yes all golden rectangles are simalar as well as their ratios
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No, not all rectangles are similar because the proportions are different.
Two rectangles are similar if corresponding angles are equal and the corresponding sides are proportional.
Yes, all rectangles are parallelograms. However, not all parallelograms are rectangles.
In fact, some are rectangles, but not all are.
All squares are rectangles also, but not all rectangles are squares, only equilateral rectangles are considered square.