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:
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 : 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."
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.
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.
1 sum of two angles equals 1800
Answer : This figure is a trapezoid as the top and the bottom lines are parallel, but not of equal lengths
'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.
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.