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.