Final answer:
A square is always a rectangle because it meets all the criteria of a rectangle, but not all rectangles are squares. The diagonals of a rhombus are always perpendicular, while the diagonals of a rectangle are always equal. The diagonals of a trapezoid being equal depends on whether it is isosceles or not.
Step-by-step explanation:
The question pertains to the properties of geometric shapes and involves understanding the relationship between the sides, angles, and diagonals of squares, rectangles, rhombuses, and trapezoids. A square is indeed a rectangle because it has all the properties of a rectangle: four right angles and opposite sides that are parallel and equal in length. However, a rectangle is not always a square as it does not require all four sides to be equal. For statement a., the diagonals of a rhombus are indeed perpendicular to each other.
Statement b. is true because the diagonals of a rectangle are equal in length. Statement c., regarding the diagonals of a trapezoid, is sometimes true, as it depends on the specific shape of the trapezoid; in an isosceles trapezoid, the diagonals are equal, but this is not the case for all trapezoids.