“A square is a rhombus but a rhombus is not a square.”
This statement is true as the definition of a rhombus is that it has 4 equal sides and the diagonally opposite sides are of equal angles. A square has 4 equal sides, and since all the angles are 90º, a square can be considered a rhombus. However, in order to be a square, all 4 angles needs to be 90º, and not all rhombuses have all 4 angles of 90º, thus not all rhombuses are squares.
The answer is D, all of the above. A square and a parallelogram are 4-sided figures, thus they are quadrilaterals. The rule of squares and parallelograms states that the opposite sides must be parallel. A trapezoid has one pair of parallel sides, the top and bottom or sometimes the left and the right.
“All parallelograms are squares.”
I do not agree with this statement. For a figure to be a square, there must be 4 equal parallel sides and 4 angles of 90º. A parallelogram does not need to have 4 equal sides, only the opposite sides need to be equal. It also does not need to have 4 angles of 90º, as long as apposite angles are equal. It is true that some parallelograms are squares and all squares are parallelograms, but not all parallelograms are squares.