**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'.

__Answer : ____Yes, the statement is justified by the statement which the Mentor mentioned, "A rhombus is a parallelogram, but all four sides have the same length."__

**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

__Answer : ____D ) All the above__

__Examples : ____A ) ____A square and parallelogram have four sides, so they are considered as quadrilaterals.__

__ ____ ____B ) ____A square and parallelogram must have sides that are parallel, otherwise, they aren't even considered as squares ____ ____ and parallelograms anymore.__

__ ____ ____C ) ____The top side and the bottom side of the trapezoid are parallel.__

**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**.

^{1 }sum of two angles equals 180^{0}

Answer :This figure is a trapezoid as the top and the bottom lines are parallel, but not of equal lengths

**Question 4:**

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

Justify your answer with example/s.

Answer :No, I do not agree with this statement as squares require all sides to be of the same length, whilst not all parallelograms have all sides which are of the same length.

**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.

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