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'.
A rhombus has 2 pairs of parallel lines and the length of all the sides are equal. A square has 2 pairs of parallel lines, the length of all the sides are equal and has 4 right angles. Since the properties of the square fall under the properties of the rhombus, the square is considered a special type of rhombus.
'All parallelograms are squares?' Do you agree with this statement?
Justify your answer with example/s.
No, I do not agree with this statement. Just like all surgeons are doctors but not all doctors are surgeons, all squares are parallelograms but not all parallelograms are squares. In order for a parallelogram to be a square as well, it must have 2 pairs of parallel sides, 4 right angles and 4 sides of equal lengths.
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.
If BFDE must be a parallelogram, its opposite sides must be of equal length and are parallel to each other. Since E is the midpoint of AD and F is the midpoint of BC, the length of BE should be the same as the length of DF and BE should also be parallel to DF. BF is confirmed parallel to DE. From all these reasons, BFDE must be a parallelogram.