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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°?

**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.

**☛ Related Questions:**

- Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
- The measures of two adjacent angles of a parallelogram are in the ratio 3:2. Find the measure of each of the angles of the parallelogram.
- Two adjacent angles of a parallelogram have equal measure. Find the measure of each of the angles of the parallelogram.
- The adjacent figure HOPE is a parallelogram. Find the angle measures x, y and z. State the properties you use to find them.

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