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

Answer :

(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.

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