Dear Mr Ng,
The question to answer:
Reasons: Statement A: Squares and parallelograms have 4 sides each. Proof:
Mentor: Great! We've already learned that quadrilaterals have how many sides?
Statement B: Opposite sides of a square and parallelogram are parallel. Proof:
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.
Statement C: A trapezoid has only one pair of parallel sides. Proof:
The shape of a trapezium shows only one pair of parallel sides.
Reasons: A parallelogram has 2 pairs of parallel lines, but the pairs of lines have different lengths (Let's say AB//CD and BC//AD. AB and CD have the same length (xcm) and BC and AD also have the same length but this time not xcm (example ycm)). Futhermore, all of the angles in a square are 90º. But in a parallelogram, opposite angles are the same.
A parallelogram has 2 parallel pair of lines (BF//ED and BE//ED). Thus BFED is a parallelogram.