1. ‘A square is a rhombus but a rhombus is not a square’.
I agree with this statement. A square is a rhombus as it has 4 lines of equal length and 2 pairs of parallel lines. A rhombus is not a square as a square has to have four equal right angles, however, a rhombus does not have to have 4 equal right angles.
2. A ) A square and a parallelogram are quadrilaterals.
This is true. Both a square and parallelogram are four sided figures and their angles adds up to 360 degrees.
B ) Opposite sides of a square and a parallelogram are parallel.
This is true. Both square and parallelogram are 4 sided figures that has 2 pairs of parallel lines.
C ) A trapezoid has one pair of parallel sides.
This is true. A trapezoid has only one pair of parallel side.
Since all of the above choices are true, this statement is also correct.
4. ‘All parallelograms are squares?
I do not agree with this statement. A parallelogram may not be a square. Parallelograms can be squares only if its four sides are of equal length, the four lines are parallel to each other and the angles in the parallelogram are all 90 degrees each.
5. 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.
Since ABCD is a parallelogram, it has to have 2 pairs of parallel lines. Since BF and DE is part of lines BC and AD respectively, it also has to parallel to each other. Lines BE and FD are also parallel as the opposite angles inside BFDE are equal. So in conclusion, figure BFDE is a parallelogram.