Questions 1,2 and 4 by Naveena Menon

1. 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’.Ans:This statement is justified because though both shapes are 4-sided polygons, the angles at the corners of a square are always 90° but the angles at the corners of a rhombus are not always at 90°.
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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

A) A square and a parallelogram are quadrilaterals. - This statement is correct as the quadrilaterals are any 4-sided polygon and both a square and a parallelogram are 4-sided polygons.

B) Opposite sides of a square and a parallelogram are parallel. - This statement is true because opposite sides of a square and a parallelogram will never meet.

C) A trapezoid has one pair of parallel sides. -This statement is true.

Ans: Hense, D(All the above) is the answer.

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4. ‘All parallelograms are squares?’ Do you agree with this statement?

Justify your answer with example/s.

Ans: I do not agree with the statement as the angles at the corners of a square will always be 90° but the angles at the corners of a parallelogram are not always 90°.