Question 1

"A square is a rhombus but a rhombus is not a square".

A rhombus is a quadrilateral whose four sides all have the

same length.

However, a square has four equal sides and four equal right

angles at the corners.

If a square is turned into a rhombus, it loses its four

right angle corners. Therefore, it cannot be counted as a

square. However, if the rhombus is turned into a square, it

retains its length and still counts as a rhombus.

Question 2:

Which of the given statements is correct? Justify your

answers with examples.

A ) A square and a parallelogram are quadrilaterals.

Correct, because a square has 4 sides and 4 corners, and so

does a parallelogram.

B ) Opposite sides of a square and a parallelogram are

parallel.

For the square, it is correct as 4 corners are supposed to

be 90°.

For the parallelogram, it is also correct because even

though it does not have 4 equal angles, it still has 2 sets

of parallel lines.

href='http://img269.imageshack.us/i/trapezium.png/'><img

src='http://img269.imageshack.us/img269/5461/trapezium.png'

border='0'/></a>

C ) A trapezoid has one pair of parallel sides.

Correct as well, refer to diagram below.

href='http://img237.imageshack.us/i/squareparallelogram.png/'><img

src='http://img237.imageshack.us/img237/9694/squareparallelogram.png'

border='0'/></a>

D ) All the above

Question 4

"All parallelograms are squares?" Do you agree with this

statement?

I do not agree with this statement. A parallelogram refers

to a figure with 2 sets of parallel lines. However, a square

has 2 sets of parallel lines, 4 sides of the same length AND

must have the corner angles equal to 90° each. A rectangle

has 2 sets of parallel lines. However, it does not have 4

equal sides. Another example is a rhombus. A rhombus has 2

sets of parallel lines. However, it again does not have 4

corner angles, making it not qualify as a square.