Read through the conversation between a mentor and a student.

**Question 1:**

Read through the conversation between a mentor and a student.

**Does anyone recall or know what we call it when 2 lines run side-by-side and never cross?**

Mentor:

Mentor:

**Yes. Lines like that are called**

Student:

Student:

__parallel__lines.

**Great! We've already learned that quadrilaterals have how many sides?**

Mentor:

Mentor:

**Four.**

Student:

Student:

**That's right and we call quadrilaterals with parallel sides**

Mentor:

Mentor:

__parallelograms__.

**But, how can all the sides be parallel if a quadrilateral is a polygon and is all closed off?**

Student:

Student:

**Great thinking! I guess what I should have said is that a parallelogram has two pairs of opposite sides that are parallel, like this:**

Mentor:

Mentor:

**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.

**So a rhombus is a type of parallelogram just like a banana is a type of fruit.**

Student:

Student:

**Right, we should not say that all parallelograms are rhombi, just like we don't say that all fruits are bananas.**

Mentor:

Mentor:

__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 supplementary^{1}. **Identify this figure, and justify your answer with reasons**.

Entry #21

ReplyDeletethanks Yu Chong