A student makes the following conjecture about quadrilaterals:
"If two quadrilaterals have their four sides equal respectively, then the two quadrilaterals are congruent."
(i) State what it means for two plane figures to be congruent.
(ii) Draw a square of side 5cm. Next, draw a rhombus whose all sides are also 5cm but whose one interior angle is 60∘. Clearly mark all equal sides in each diagram.
(iii) Using appropriate geometric reasoning, explain why the square and the rhombus constructed in part (ii) are not congruent even though their corresponding sides are equal. Hence, show that these two figures provide a counterexample to the student’s conjecture.