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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°?

Name: 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°?
Uploaded: 2020-05-12T12:54:30Z
Duration: 4 min 53 s
Description: Let's look into a quadrilateral ABCD and check if it is a parallelogram using the following conditions: (i) For, ∠D + ∠B = 180°, ABCD may or may not be a parallelogram (ii) For, AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm, ABCD cannot be a parallelogram (iii) For, ∠A = 70° and ∠C = 65°, ABCD cannot be a parallelogram.

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.

☛ Check: NCERT Solutions for Class 8 Maths Chapter 3

Video Solution:

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°?

NCERT Solutions Class 8 Maths Chapter 3 Exercise 3.3 Question 3

Summary:

Let's look into a quadrilateral ABCD and check if it is a parallelogram using the following conditions: (i) For, ∠D + ∠B = 180°, ABCD may or may not be a parallelogram (ii) For, AB = DC = 8 cm, AD = 4 cm and BC = 4.4 cm, ABCD cannot be a parallelogram (iii) For, ∠A = 70° and ∠C = 65°, ABCD cannot be a parallelogram.

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