question_answer 16)

                Can a quadrilateral ABCD be parallelogram if                 (i) \[\angle D+\angle B={{180}^{\text{o}}}\]                 (ii) \[AB=DC=8\text{ }cm,\text{ }AD=4\text{ }cm\] and \[BC=4.4\text{ }cm\]                 (iii) \[\angle A={{70}^{\text{o}}}\] and \[\angle C={{65}^{\text{o}}}\].

Answer:

                (i) Can be, but need not be (ii) No; in a parallelogram, opposite sides are equal; but here, \[AD\ne BC\]. (iii) No; in a parallelogram, opposite angles are equal; but here \[\angle A\ne \angle C\].