Question 2, 4, 5

2) 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

  The answer is D. For A, quadrilaterals are 2-dimensional figures with 4 straight sides, and the interior angles add up to 360 degrees. Examples of quadrilaterals are squares, parallelograms, and kites. Since a square and a parallelogram are 2-dimensional figures with 4 straight sides, and the interior angles add up to 360 degrees, they are quadrilaterals. For B, squares have 2 pairs of parallel lines, while a parallelogram has a pair of parellel line at each side. Hence, opposite sides of a square and a parallelogram are parallel. For C, a trapezoid has only a pair of parellel lines. If there were more than a pair of parallel lines, it would be a parallelogram. So, all of the statements are correct.

4) All parallelograms are squares?' Do you agree with this statement?

Justify your answer with example/s.

  No, not all parallelograms are squares. Some parallelograms have internal angles which are not all 90 degrees, while all squares have 4 angles with 90 degrees. Also, a pair of lines of a parallelogram would have a different length than the other pair of lines. All of the squares' lines are equal in length, which proves again that not all parallelograms are squares.

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.

 A parallelogram is a figure with 2 pairs of parallel lines. Since figure BFDE has 2 pairs of parellel lines, it is a parallelogram.

Preston