A geometry learner claims: “If two angles of a quadrilateral are equal, the quadrilateral must be a parallelogram.” Test this claim by constructing a suitable figure and reasoning about its properties.
(i) Draw (with reasonable accuracy) a quadrilateral in which exactly one pair of opposite angles is equal but the other conditions needed for a parallelogram are not met.
(ii) Measure all four sides and all four angles of the quadrilateral you have drawn. Record your results.
(iii) Using your measurements, explain why the quadrilateral you constructed is not a parallelogram even though it satisfies the “equal angles” condition.
(iv) State clearly how this single quadrilateral serves as a counterexample that invalidates the learner’s original claim.