(i) A student says, “If a quadrilateral has a pair of opposite sides that are equal, it must be a parallelogram.” Explain with reasons whether the statement is always true.
(ii) The same student later claims, “If a quadrilateral has a pair of opposite sides that are parallel, it must be a parallelogram.” Explain with reasons whether this second claim is always true.
(iii) Using your observations from (i) and (ii), justify why the simultaneous conditions “one pair of opposite sides equal and parallel” together guarantee that the quadrilateral is a parallelogram.