A rectangle is a quadrilateral with four right angles. A square is a special type of rectangle where all four sides are equal in length. Therefore, statement D is true: all squares are rectangles.
A parallelogram is a quadrilateral with opposite sides that are parallel. A rectangle has opposite sides that are parallel, so statement B is true: all rectangles are parallelograms.
A rhombus is a quadrilateral with all sides of equal length. It also has opposite sides that are parallel. Since a parallelogram has opposite sides that are parallel, statement C is true: all rhombuses are parallelograms.
However, not all parallelograms are rectangles or squares. A parallelogram can have angles that are not right angles, unlike a rectangle or a square. Therefore, statement A is false: not all rectangles are squares.
Similarly, not all squares are rhombuses. While a square is a rhombus because it has all sides of equal length, a rhombus does not necessarily have all angles that are right angles like a square does. So, statement E is false: not all squares are rhombuses.
Lastly, a trapezoid is a quadrilateral with one pair of parallel sides. A parallelogram has two pairs of parallel sides, so a trapezoid is not necessarily a parallelogram. Therefore, statement F is false: not all trapezoids are parallelograms.
To summarize:
- All squares are rectangles (D is true).
- All rectangles are parallelograms (B is true).
- All rhombuses are parallelograms (C is true).
- Not all rectangles are squares (A is false).
- Not all squares are rhombuses (E is false).
- Not all trapezoids are parallelograms (F is false).