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# 3.Can a quadrilateral ABCD be a parallelogram if (i) $$∠D + ∠B = 180^{\circ}?$$ (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii)$$∠A = 70^{\circ} and ∠C = 65^{\circ}?$$

(i) For ∠D + ∠B = $$180^{\circ}$$, quadrilateral ABCD may be a parallelogram if the sum of measures of adjacent angles is $$180^{\circ}$$ and also the opposite angles should be of same measures. So here, ABCD can be but need not be a parallelogram.

(ii) Given: AB = DC = 8 cm, AD = 4 cm, BC = 4.4 cm

In general the opposite sides od a parallelogram is equal.

But here, $$AD \neq BC$$

Thus, ABCD cannot be a parallelogram.

(iii) $$∠A = 70^{\circ} and ∠C = 65^{\circ}$$

Since $$∠A \neq ∠C\quad$$[Opposite angles of quadrilateral are not equal.]

Hence, ABCD is not a parallelogram.