Question 1, 2 and 4 - Loh Cheng Ngee

1) ‘A square is a rhombus but a rhombus is not a square’.
This statement is true. The properties of a square are that there are 2 pairs of parallel lines and there are 4 right angles while the properties of a rhombus are that no defined angles for each of the 4 and that there are 2 pairs of parallel lines. Since a rhombus can have 4 right angles, a square is a rhombus in that situation. A rhombus however cannot be a square as a square has defined 4 right angles while there are no given defined angles for the rhombus as the angles of the 2 pairs of parallel lines will be different.

2) D is correct. A square and a parallelogram are quadrilaterals as they both have 4 sides to them, as they have 4 angles in the square and parallelogram. Opposite sides of a square and a parallelogram are parallel as they both have 2 pairs of parallel lines, so each ‘pair’ of a side in the 2 quadrilaterals will definitely be parallel. A trapezoid has only one pair parallel sides as the two angles of the vertical lines add up to 180 degrees. If it were in any other way, they would not add up to 180 degrees.

4) I do not agree with the statement. Parallelograms are not squares as although the opposite sides are parallel, the length of the opposite sides are different. They must be different as the angles of the parallelogram will change, and a square has the same length for all 4 sides, therefore parallelograms cannot be squares.