__Question__1:

A conversation between a mentor and a student.A 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:Student:

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

Mentor:Mentor:

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

'A square is a rhombus but a rhombus is not a square'. Is this true? A rhombus is a special type of square, but a square is not a rhombus.

Why is that so? A square has 4 sides and 2 lines side by side will meet at the angle of 90 degrees. While the rhombus lines side by side will meet at any angle.

Just to add on. Lines at the sides are parallel at both rhombus and 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**

*Ans:*

*All of the above*

**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****.**

*Ans:*

It is a trapezium. A trapezium has pair of parallel lines, however, the other pair is not equal and parallel, thus it would look something like this:

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*Question 4:*

'All parallelograms are squares?' Do you agree with this statement?

Justify your answer with example/s.Ans:Yes, all four sides of the squares areparallelogram

Question 5:

ABCD is a parallelogram. If E is midpoint of AD and F is midpoint of BC show, with reasons, that BFDE must be a parallelogram.

**The key property of a parallelogram has four sides, each line directly opposite is parellel. BFDE has this key property, thus, it is a parallelogram.**

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Aaron Sng S1-08 (18)

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