### Question 1,2 and 4. Grace Tan Soo Woon

Q1. Based on the above conversation discuss, with examples and justification whether the following statement is justified.

‘A square is a rhombus but a rhombus is not a square’.

Answer: The properties of a rhombus is that the lines must of equal length and the opposite lines must be parallel. The properties of a square is that all line must be of equal length, opposite sides must be parallel and that all the angles in the square must be equal (90 degrees every corner).

A square is a type of rhombus as it fulfills all the properties needed. On the other hand, the rhombus cannot be a square as the angles in the rhombus can be of any angle as long as the opposite angle is the same and the top and bottom angle has to add up to 180 degrees.

Q2. Which of the given statements is correct? Justify your answer/s with examples.

A ) A square and a parallelogram are quadrilaterals.

B ) Opposite sides of a square and a parallelogram are parallel.

C ) A trapezoid has one pair of parallel sides.

D ) All the above

Quadrilaterals are four sided figures. Both the square and the parallelogram have 4 sides. Thus the square and parallelogram are quadrilaterals.

The opposite sides of the square and parallelogram are parallel as their ends do not meet.

A trapezoid has one pair of parallel sides as the properties of the trapezoid are that the two angles on the same side of the trapezium always add up to 180 degrees. Other than that, there are only one pair of parallel lines, unlike squares and parallelograms which have two pairs of parallel lines.

Thus the answer is All of the Above.

Q4. ‘All parallelograms are squares?’ Do you agree with this statement?