Q1: The statement about squares being rhombuses but rhombuses not being squares is true.

A rhombus has 4 sides of equal length, with two pairs of parallel lines. A square fulfills this rule for rhombuses. However, a in order for a quadrilateral to be a square, it must have 4 sides of equal length, two pairs of parallel lines

*and*all angles must be 90 degrees. A rhombus need not have angles of 90 degrees. Thus, a rhombus is not a square.Q2: A) " A square and parallelogram are quadrilaterals " is true. A quadrilateral has 4 sides. All angles in a quadrilateral add up to 360 degrees. A parallelogram fulfills this by having 4 sides, and opposite angles which add up to 180 degrees, and both sets of opposite angles added up is 360 degrees. A square also fulfills this by having 4 sides, and four angles each being 90 degrees, all adding up to 360 degrees.

B) " Opposite sides of a square and a parallelogram are parallel " is true. In order for angles to have parallel opposite sides, it must have adjacent angles that add up to 180 degrees. A square's adjacent angles are all 90 degrees and 90 degrees, adding up to 180 degrees. A parallelogram also has adjacent angles that add up to 180 degrees, though not 90 and 90(in degrees).

C) " A trapezium has one pair of parallel sides " is true. If a quadrilateral has one pair of parallel sides, it must have sets of adjacent angles that add up to 180 degrees. The trapezium does have adjacent angles that add up to 180 degrees, so it can have one pair of adjacent sides. But as the sets of adjacent angles are not equal in degrees, the trapezium must have only one pair.

D) " All of the above " is true as all the above statements are true.

Thus the statement D is correct.

Q4: " All parallelograms are squares?" is false. In order to be a square, a quadrilateral has four sides, two pairs of parallel lines, all being equal in length, and all angles must be 90 degrees.

A parallelogram has 4 sides and is a quadrilateral. Also, it has two pairs of parallel lines. This causes adjacent angles in a parallelogram to add up to 180 degrees. However, it does not have all sides of equal length. A parallelogram also does not any angles of 90 degrees. Its adjacent angles might add up to 180 degrees like a square, but are not equal.

Thus, no parallelograms are squares. Though, vice versa is true.

Tim Yap

Very comprehensive answer just short of providing illustrations well done Tim.

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