The DAV Maths Class 8 Solutions and **DAV Class 8 Maths Chapter 12 Worksheet 4** Solutions of Construction of Quadrilaterals offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 12 WS 4 Solutions

Question 1.

Using a ruler and compasses only, construct the following:

(i) A quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = \(\overline{\mathrm{CD}}\) = 5 cm, \(\overline{\mathrm{BC}}\) = 4.5 cm, ∠B = 45°, ∠C = 135°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{AB}}\) = 5 cm.

2. Draw an angle of 45° at B and cut \(\overline{\mathrm{BC}}\) = 4.5 cm.

3. Draw an angle of 135° at C and cut \(\overline{\mathrm{CD}}\) = 5 cm.

4. Join \(\overline{\mathrm{AD}}\).

5. ABCD is the required quadrilateral.

(ii) A quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 5 cm, \(\overline{\mathrm{BC}}\) = 6 cm, \(\overline{\mathrm{CD}}\) = 6.5 cm, ∠B = 105°, ∠C = 75°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{AB}}\) = 5 cm.

2. Draw an angle of 105° at B and cut \(\overline{\mathrm{BC}}\) = 6 cm.

3. Draw an angle of 75° at C and cut \(\overline{\mathrm{CD}}\) = 6.5 cm.

4. Join D to A.

5. ABCD is the required quadrilateral.

(iii) A quadrilateral PQRS in which \(\overline{\mathrm{PQ}}\) = 5 cm, \(\overline{\mathrm{QR}}\) = 4 cm, \(\overline{\mathrm{RS}}\) = 4.5 cm, ∠Q = 90°, ∠R = 135°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{PQ}}\) = 5 cm.

2. Draw an angle of 90° at Q and cut \(\overline{\mathrm{QR}}\) = 4.5 cm.

3. Draw an angle of 135° at R and cut \(\overline{\mathrm{RS}}\) = 4.5 cm.

4. Join S to P.

5. PQRS is the required quadrilateral.

(iv) A quadrilateral MNRS in which \(\overline{\mathrm{MN}}\) = 4.5 cm, \(\overline{\mathrm{NR}}\) = 5 cm, \(\overline{\mathrm{RS}}\) = 6 cm, ∠N = 120°, ∠R = 60°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{MN}}\) = 4.5 cm.

2. Draw an angle of 120° at N and cut \(\overline{\mathrm{NR}}\) = 5 cm.

3. Draw an angle of 60° at R and cut \(\overline{\mathrm{RS}}\) = 6 cm.

4. Join S to M.

6. MNRS is the required quadrilateral.

(v) A quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = \(\overline{\mathrm{BC}}\) = \(\overline{\mathrm{CD}}\) = 6 cm and ∠B = 60°, ∠C = 120°.

Solution:

1. Draw \(\overline{\mathrm{AB}}\) = 6 cm.

2. Draw an angle of 60° at B and cut \(\overline{\mathrm{BC}}\) = 6 cm.

3. Draw an angle of 120° at C and cut \(\overline{\mathrm{CD}}\) = 6 cm.

4. Join D to A.

5. ABCD is the required quadrilateral.

Question 2.

Using a ruler, compasses, and protractor if required, construct the following:

(i) A quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 5 cm, \(\overline{\mathrm{BC}}\) = 4 cm, \(\overline{\mathrm{CD}}\) = 4.5 cm, ∠B = 70°, ∠C = 100°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{AB}}\) = 5 cm.

2. Draw an angle of 70° at B and cut \(\overline{\mathrm{BC}}\) = 4 cm.

3. Draw an angle of 100° at C and cut \(\overline{\mathrm{CD}}\) = 4.5 cm.

4. Join D to A.

5. ABCD is the required quadrilateral.

(ii) A quadrilateral PQRS in which \(\overline{\mathrm{PQ}}\) = 5 cm, \(\overline{\mathrm{QR}}\) = 6 cm, \(\overline{\mathrm{RS}}\) = 4 cm, ∠Q = 80°, ∠R = 100°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{PQ}}\) = 5 cm.

2. Draw an angle of 80° at Q and cut \(\overline{\mathrm{QR}}\) = 6 cm.

3. Draw ∠R = 100° and cut \(\overline{\mathrm{RS}}\) = 4 cm.

4. Join S to P.

5. PQRS is the required quadrilateral.

(iii) A quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 4 cm, \(\overline{\mathrm{BC}}\) = 5 cm, \(\overline{\mathrm{CD}}\) = 4.5 cm, ∠B = 85°, ∠C = 95°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{AB}}\) = 4 cm.

2. Draw an angle of 85° with protractor at B and cut \(\overline{\mathrm{BC}}\) = 5 cm.

3. Draw ∠C = 95° with protractor and cut \(\overline{\mathrm{CD}}\) = 4.5 cm.

4. Join D and A.

5. ABCD is the required quadrilateral.

(iv) A quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 4 cm, \(\overline{\mathrm{BC}}\) = 3 cm, \(\overline{\mathrm{CD}}\) = 4.5 cm, ∠B = 105°, ∠C = 80°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{AB}}\) = 4 cm.

2. Draw ZB = 105° and cut \(\overline{\mathrm{BC}}\) = 3 cm.

3. Draw ZC = 80° and cut \(\overline{\mathrm{CD}}\) = 4.5 cm.

4. Join D to A.

5. ABCD is the required quadrilateral.

(v) A quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 5 cm, \(\overline{\mathrm{BC}}\) = 4 cm, \(\overline{\mathrm{CD}}\) = 5 cm, ∠B = 80°, ∠C = 100°.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{AB}}\) = 5 cm.

2. Draw ∠B = 80° and cut \(\overline{\mathrm{BC}}\) = 4 cm.

3. Draw ∠C = 100° and cut \(\overline{\mathrm{CD}}\) = 5 cm.

4. Join D and A.

5. ABCD is the required quadrilateral.

### DAV Class 8 Maths Chapter 12 Value Based Questions

Question 1.

On a pastel sheet, construct a parallelogram of sides 45 cm and 30 cm and one of the base angles is 80°. Cut it out.

(i) Make a poster on ‘DIGITAL INDIA’, ‘MAKE IN INDIA’.

(ii) How can you contribute to ‘MAKE IN INDIA’.

Solution:

The parallelogram with given dimensions can be constructed with the following concepts.

We know that opposite sides and opposite angles of a parallelogram are equal and interior angles of the same side of a transversal are supplementary.

∴ The sides of the parallelogram will be 45 cm, 30 cm, 45 cm, and 30 cm.

One of the base angles = 80° (given)

Other base angle = 180° – 80° = 100°

∴ Angles of the Parallelogram will be 80°, 100°, 80°, 100°.

Now, the students can construct the required parallelogram on a pastel sheet themselves.

(i) Do yourself.

(ii) Making elders aware of the ‘Make in India’ concept and by identifying products that can be manufactured with a small budget we can contribute to ‘MAKE IN INDIA’.