## Thursday, August 12, 2010

### Question 1 by Chio Jia Le

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.
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'.

ANSWER: A square has all the rhombus' properties while the rhombus do not have all of the square's property. For example, a square's adjacent sides are perpendicular to each other while the rhombus' are not perpendicular. Another property is that the length of diagonals of the square are equal but the rhombus' are not the same.