Can a quadrilateral ABCD be a parallelogram if (i) &ang;D + &ang;B = 180°? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii) &ang;A = 70° and &ang;C = 65°?

Question

Can a quadrilateral ABCD be a parallelogram if (i) &ang;D + &ang;B = 180&deg;? (ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm? (iii) &ang;A = 70&deg; and &ang;C = 65&deg;?

Philoid · Accepted Answer

(i) Considering, ∠D + ∠B = 180°, quadrilateral ABCD may or may not be a parallelogram

Along with this, the following criteria should also be fulfilled

Opposite angles should also be of same measures

The sum of the measures of adjacent angles should be 180°

(ii) No because opposite sides AD and BC are of different lengths

(iii) No as opposite angles A and C have different measures

Can a quadrilateral ABCD be a parallelogram if(i) ∠D + ∠B = 180°?(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?(iii) ∠A = 70° and ∠C = 65°?

Can a quadrilateral ABCD be a parallelogram if

(i) ∠D + ∠B = 180°?

(ii) AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm?

(iii) ∠A = 70° and ∠C = 65°?