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.
1sum of two angles equals 180 degrees.
Ans: This quadrilateral is a trapezium. The definition of a trapezium is that it has at least one set of parallel lines, without considering the fact whether the length of the lines are equal, or if the other two lines are parallel to each other or they must be of a certain length.
‘All parallelograms are squares?’ Do you agree with this statement?
Justify your answer with example/s.
Ans: No, I do not agree that all parallelograms are squares. The definition of square is that it must have all four of its corners at a right angle, and not all parallelograms meets this criteria.
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.
Ans: The criteria of a parallelogram is that there must be 2 pairs of parallel lines. Since BF has the same length as ED, and they are parallel to each other, BE and FD should also be of the same length and are parallel to each other. Hence BFDE must be a parallelogram.