Question

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

Answer 1

Answer:

cuemath_logo

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°?

Solution:

(i) Using the angle sum property of a quadrilateral,

∠A + ∠B + ∠D + ∠C = 360°

∠A + ∠C + 180° = 360° (Since its given that ∠D + ∠B = 180°)

∠A + ∠C = 360° -180°

∠A + ∠C = 180° (Opposite angles should also be of same measures.)

For ∠D + ∠B = 180°, is a parallelogram.

If the following conditions are fulfilled, then ABCD is a parallelogram. The sum of the measures of the adjacent angles should be 180° and opposite angles should also be of the same measure.

Hence, using the given condition ∠D + ∠B = 180° we can say that yes, it may or may not be a parallelogram.

(ii) Property of parallelogram: The opposite sides of a parallelogram are of equal length.

Here, AD = 4cm and BC = 4.4 cm

Opposite sides AD and BC are of different lengths. So, ABCD is not a parallelogram

(iii) Property of a parallelogram: In a parallelogram opposite angles are equal.

So, ∠A = 70° and ∠C = 65°

Opposite angles are not equal. So, ABCD is not parallelogram.

Answer 2

Answer:

ABCD be a parallelogram if

i) D+B=180°?