Since a square fulfills the definition of a rectangle, we know that a square is in fact a rectangle. The given statement is true.
b A parallelogram is defined as a quadrilateral with two pairs of parallel sides. This is the only definition a polygon has to fulfill to be called a parallelogram. However, if a quadrilateral is a parallelogram, it needs to have two pairs of parallel sides.
This means the given statement is false.
c A parallelogram is defined as a quadrilateral with two pairs of parallel sides. Let's draw a arbitrary rhombus and check if this criteria holds true for the shape.
Since a rhombus fulfills the definition of a parallelogram, we know that all rhombi are also parallelograms and the given statement is true.
d A rhombus is defined as a quadrilateral with two pairs of parallel sides and four congruent sides. Let's draw an arbitrary square and check if these criteria hold true for the shape.
Since a square fulfills the definition of a rhombus, we know that all squares are also rhombi. This means the given statement is true.
e If the diagonals of a parallelogram bisect the angles, they cut them in two equal halves. Let's draw an arbitrary parallelogram and one of the diagonals.
