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.
Mentor: Great! We've already learned that quadrilaterals have how many sides?
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:
(picture)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: This statement is true, as the definition of a rhombus is that opposite sides are parallel to each other, and a square fulfills this definition. However, a square must not only have its opposite sides parallel to each other, the corners must be at a right angle, which means that the not all rhombuses can be a square.
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 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 supplementary1. Identify this figure, and justify your answer with reasons.
Answer: This quadrilateral is a trapezium, as definition of a trapezium has at least one set of parallel lines, without stating whether the length of the lines have to be equal, or if the other two lines are parallel to each other or must be of a certain length.
**1 sum of two angles equals 1800
'All parallelograms are squares?' Do you agree with this statement? Justify your answer with example/s.
Answer: No, not all parallelograms are squares. Square must have its corners at a right angle, but not all parallelograms fulfill this condition.
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.
Answer: BF has the same length as ED, and they are parallel to each other, which means that BE and FD are also of the same length and are parallel to each other. When both sets of lines are parallel and have the same length as each other, it will be called a parallelogram.