A square is a rhombus but a rhombus is not a square.
I agree with this statement.
The square and the rhombus share similar properties. Both the square and the rhombus has 4 equal side, opposites which are parallel, the sum of the supplementary angles is 180°, and the opposite angles are equals.
However, not all rhombi are squares. A rhombus may not always have right angles.
All parallelograms are squares.
I disagree with this statement.
The parallelogram and the square share similar properties. Both the parallelogram and the square have their opposite sides of the same length, which are parallel, the sum of the supplementary angles is 180°, and the opposite angles are equal.
However, not all parallelograms are squares as the lengths of all 4 sides may differ.
BFDE must be a parallelogram.
According to the picture, the length of BC and AD is x. So, the length of ED and BF must be 1/2 x. Since ED and BF are of the same length as are parallel, we can conclude that BE and DF are both parallel and of the same length.