*1) ‘A square is a rhombus but a rhombus is not a square’.*

A square must have four sides of equal length and four right angles. The angles must be 90 degrees. The opposite sides are also parallel.

A rhombus must have four sides of equal length. The opposite sides are also parallel. The opposite angles of a rhombus are the same. However, the angles must not only be 90 degrees but can differ.

Hence, a square can be a rhombus as all it’s properties fulfil the ones of a rhombus. However, a rhombus is not a square as the angles can differ. It might not be 90 degrees, which is needed to fulfil the requirements to be a square.

2) 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

- Properties of a square- A square must have four sides of equal length and four right angles. The angles must be 90 degrees. The opposite sides are also parallel.

Properties of a parallelogram- A parallelogram has two pairs of parallel sides. The opposite angles are the same and the opposite sides are of the same length.

Properties of a trapezium- A trapezium have a pair of parallel sides.

Firstly, quadrilaterals are four sided figures that are made out of four straight lines. A square and a parallelogram both have four sides that are straight lines. Hence, they are quadrilaterals.

Next, the properties of a square and a parallelogram both include ‘opposite sides are parallel’. Hence, statement B is true.

Besides that, the properties of a trapezium also state that it must have one pair of parallel sides. Hence, statement C is true.

Question 4:

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

Justify your answer with example/s.

No. A square must have four sides of equal length and four right angles. The angles must be 90 degrees. The opposite sides are also parallel. A parallelogram has two pairs of parallel sides. The opposite angles are the same and the opposite sides are of the same length.

The angles in a square must be 90 degrees. However, the angles in a parallelogram can differ. There can also be two different angles in a parallelogram. The lengths each side of a parallelogram can differ while the sides of a square must be the same. Hence, not all parallelograms are squares as not all of them fulfil the properties of a square.

Parallelogram- Does not have 90 degree angles.

Source- http://giraffian.com/pictionary-files/p/parallelogram.png

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