Question 1:     
Read through the conversation between a mentor and a student. 
Mentor:     Does anyone recall or know what we call it when 2 lines run side-by-side and never cross?
Student:    Yes. Lines like that are called parallel lines.
Mentor:     Great! We've already learned that quadrilaterals have how many sides? 
Student:    Four.
Mentor:     That's right and we call quadrilaterals with parallel sides parallelograms.
Student:    But, how can all the sides be parallel if a quadrilateral is a polygon and is all closed off? 
Mentor:      Great thinking! I guess what I should have said is that a parallelogram has two pairs of opposite sides that are parallel, like this:

Student:     Oh, so the top is parallel to the bottom and the sides are parallel to each other. I understand now!

Mentor:      Good. Now I want to tell you about a special kind of parallelogram. It's called a rhombus. A rhombus is a parallelogram, but all four sides have the same length.
Student:     So a rhombus is a type of parallelogram just like a banana is a type of fruit.
Mentor:      Right, we should not say that all parallelograms are rhombi, just like we don't say that all fruits are bananas.

   Question for discussion

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'.

I believe that this statement is true. A rhombus is a figure that has opposite sides that are parallel to each other. A square happens to fall in that category. However a square must have all internal angles at 90 degrees before it can be called a square. However, not all rhombuses have 90 degree corners, so not all rhombuses can be a square.

Question 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

The correct statements are: D

A is correct as both the square and the parallelogram have 4 sides, and a quadrilateral figure has 4 sides. Thus, this statement is correct. 

B is also correct as it is a fact that the opposite sides of a square and parallelogram are parallel. 

C is also correct as it is also a fact that a trapezoid has a pair of parallel sides. 

Since all the statements are correct the correct statement is D. 

Question 3:

A quadrilateral is drawn on a piece of paper. It has one pair of opposite sides equal in length, the other pair not equal in length, and a pair of opposite angles that are supplementary¹. Identify this figure, and justify your answer with reasons.

This figure is a trapezium. A trapezium fits the description. It could have a pair of opposite sides that are equal in length, and it also could have another pair which are not equal in length. The other quadrilateral figures do not fit this description as all of the figure's opposite sides are equal in length, with the exception of the kite. The trapezium also has a pair of opposite angles that are supplementary. Since the trapezium fits this description the best, the figure should be the trapezium. 

Done by: Lee YuChong S1-09 (17)