Question

Can a quadrilateral \(ABCD\) be a parallelogram if 

1. \(\angle D + ∠B = 180°\)? 
2. \(AB = DC = 8 \;cm\), \(AD = 4 \;cm\) and \(BC = 4.4 \;cm\)? 
3. \(∠A = 70°\) and \(∠C = 65°\)?

Answer 1

(i) For \(∠ D + ∠ B = 180°\), quadrilateral \(ABCD\) may or may not be a parallelogram. 
Along with this condition, the following conditions should also be fulfilled.
The sum of the measures of adjacent angles should be \(180\degree\).
Opposite angles should also be of the same measures.

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(ii) No. 
Opposite sides \(AD\) and \(BC\) are of different lengths.

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(iii) No. 
Opposite angles \(A\) and \(C\) have different measures.