The DAV Maths Class 8 Solutions and **DAV Class 8 Maths Chapter 12 Worksheet 1** Solutions of Construction of Quadrilaterals offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 12 WS 1 Solutions

Question 1.

Construct a quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 4 cm, \(\overline{\mathrm{BC}}\) = 5 cm, \(\overline{\mathrm{CD}}\) = 4.5 cm, \(\overline{\mathrm{AD}}\) = 5.5 cm and diagonal \(\overline{\mathrm{AC}}\) = 7.5 cm. Measure diagonal \(\overline{\mathrm{BD}}\).

Solution:

Steps of Construction:

1. Draw AB = 4 cm.

2. Draw arcs from A and B with radii 7.5 cm and 5 cm respectively which meet at C.

3. Join \(\overline{\mathrm{AC}}\) and \(\overline{\mathrm{BC}}\).

4. Draw two arcs from A and C with radii 5.5 cm and 4.5 cm respectively to meet at D.

5. Join \(\overline{\mathrm{AD}}\) and \(\overline{\mathrm{CD}}\) and \(\overline{\mathrm{BD}}\).

6. ABCD is the required quadrilateral and \(\overline{\mathrm{BD}}\) = 6 cm.

Question 2.

Construct a quadrilateral PQRS in which sides \(\overline{\mathrm{PQ}}\) = 3 cm, \(\overline{\mathrm{QR}}\) = 4 cm, \(\overline{\mathrm{RS}}\) = 3.5 cm,

\(\overline{\mathrm{SP}}\) = 4 cm and diagonal \(\overline{\mathrm{PR}}\) = 5 cm. Measure ∠PQR using a protractor.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{PQ}}\) = 3 cm.

2. Draw arcs from P and Q with radii 5 cm and 4 cm respectively to meet at R.

3 Join \(\overline{\mathrm{PR}}\) and \(\overline{\mathrm{QR}}\).

4. Draw arcs from P and R with radii 4 cm and 3.5 cm respectively to meet at S.

5. Join PS and RS.

6. PQRS is the required quadrilateral.

7. ∠PQR = 90°.

Question 3.

Construct a quadrilateral ABCD in which sides \(\overline{\mathrm{AB}}\) = \(\overline{\mathrm{BC}}\) = 4 cm, \(\overline{\mathrm{CD}}\) = \(\overline{\mathrm{AD}}\) = 5 cm and diagonal \(\overline{\mathrm{AC}}\) = 6.5 cm. Draw diagonal \(\overline{\mathrm{BD}}\) and measure it.

Solution:

Steps of Construction:

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

2. Draw arcs from A and B with radii 6.5 cm and 4 cm respectively to meet at C.

3. Join \(\overline{\mathrm{AC}}\) and \(\overline{\mathrm{BC}}\).

4. Draw arcs from A and C with a radius 5 cm each respectively to meet at D.

5. Join \(\overline{\mathrm{AD}}\) and \(\overline{\mathrm{CD}}\).

6. ABCD is the required quadrilateral.

7. Join \(\overline{\mathrm{BD}}\) which is equal to 6.5 cm.

Question 4.

Construct a quadrilateral ABCD in which each side is 4.5 cm and one diagonal \(\overline{\mathrm{AC}}\) = 6 cm. Measure \(\overline{\mathrm{BD}}\).

Solution:

Steps of Construction:

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

2. Draw arcs from A and B with radii 6 cm and 4.5 cm respectively to meet at C.

3. Draw two arcs from A and C with a radius of 4.5 cm each to meet at D.

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

5. ABCD is the required quadrilateral.

6. Join \(\overline{\mathrm{BD}}\) which is equal to 6 cm.

Question 5.

Construct a quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 4 cm, \(\overline{\mathrm{BC}}\) = 3 cm. \(\overline{\mathrm{CD}}\) = 4 cm, \(\overline{\mathrm{AD}}\) = 3 cm and diagonal \(\overline{\mathrm{AC}}\) = 5 cm. Measure diagonal \(\overline{\mathrm{BD}}\). Is it equal to \(\overline{\mathrm{AC}}\)? Measure ∠A.

Solution:

Steps of Construction:

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

2. Draw arcs from A and B with radii 5 cm and 3 cm respectively to meet at C.

3. Join \(\overline{\mathrm{AC}}\) and \(\overline{\mathrm{BC}}\).

4. Draw two arcs from A and C with radii 3 cm and 4 cm respectively to meet at D.

5. Join \(\overline{\mathrm{CD}}\) and \(\overline{\mathrm{AD}}\).

6. ABCD is the required quadrilateral.

7. Join \(\overline{\mathrm{BD}}\) and \(\overline{\mathrm{BD}}\) = 5 cm.

8. Yes \(\overline{\mathrm{AC}}\) and \(\overline{\mathrm{BD}}\) = 5 cm

9. ∠A = 90°.

Question 6.

Construct a quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = \(\overline{\mathrm{CD}}\) = 5 cm, \(\overline{\mathrm{BC}}\) = \(\overline{\mathrm{AD}}\) = 4 cm and \(\overline{\mathrm{BD}}\) = 6.5 cm.

Solution:

Steps of Construction:

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

2. Draw arcs from A and B with radii 4 cm and 6.5 cm respectively to meet at D.

3. Join \(\overline{\mathrm{AD}}\) and \(\overline{\mathrm{BD}}\).

4. Draw arcs from D and B with radii 5 cm and 4 cm respectively to meet at C.

5. Join \(\overline{\mathrm{BC}}\) and \(\overline{\mathrm{DC}}\).

6. ABCD is the required quadrilateral.

### DAV Class 8 Maths Chapter 12 Worksheet 1 Notes

Construction of a triangle can be done if

- the measure of its three sides are given. Or
- the measure of two angles and one side are given. Or
- the measure of two sides and one angle are given. Or
- one side and the hypotenuse of a right triangle are given.

Construction of a quadrilateral can be done if the measure of 4 sides or 3 sides and one angle or 2 sides and 2 angles or one diagonal and 3 sides are given.

Example 1.

Construct a quadrilateral PQRS if \(\overline{\mathrm{PQ}}\) = 3.5 cm, \(\overline{\mathrm{QR}}\) = 4.5 cm, \(\overline{\mathrm{RS}}\) = 5 cm,

\(\overline{\mathrm{PS}}\) = 5.5 cm, \(\overline{\mathrm{PR}}\) = 6 cm.

Solution:

Steps of Construction:

- Draw \(\overline{\mathrm{PR}}\) = 6 cm.
- Draw two arcs from P and R with radius 3.5 cm and 4.5 cm respectively to meet at Q.
- Join \(\overline{\mathrm{PQ}}\) and \(\overline{\mathrm{RQ}}\).
- Draw two arcs from P and R with radius 5.5 cm and 5 cm respectively to meet at S.
- Join \(\overline{\mathrm{PS}}\) and \(\overline{\mathrm{RS}}\).
- □PQRS is the reauired quadrilateral.

Example 2.

Construct a quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 4 cm, \(\overline{\mathrm{BC}}\) = 5 cm, \(\overline{\mathrm{CD}}\) = 4.5 cm and the diagonal \(\overline{\mathrm{AC}}\) = 6.5 cm and \(\overline{\mathrm{BD}}\) = 7.5 cm.

Solution:

Steps of Construction:

- Draw \(\overline{\mathrm{AB}}\) = 4 cm.
- Draw two arcs from B and A with radius 5 cm and 6.5 cm respectively to meet at C.
- Join \(\overline{\mathrm{AB}}\) and AC.
- Draw two arcs from B and C with radius 7.5 cm and 4.5 cm respectively to meet at D.
- Join \(\overline{\mathrm{BD}}\) and \(\overline{\mathrm{CD}}\) and \(\overline{\mathrm{AD}}\).
- □ABCD is the required quadrilateral.

Example 3.

Construct a quadrilateral PQRS in which \(\overline{\mathrm{PQ}}\) = 3.5 cm, \(\overline{\mathrm{QR}}\) = 5 cm, ∠P = 750, ∠Q = 90° and ∠R = 120°.

Solution:

Steps of Construction:

- Draw \(\overline{\mathrm{PQ}}\) = 3.5 cm.
- Draw the angles of 75° at P and 90° at Q.
- Draw \(\overline{\mathrm{QR}}\) = 5 cm
- Draw an angle of 120° at R which meets the angle line of 75° at S.
- □PQRS is the required quadrilateral.

Example 4.

Construct a DABCD in which \(\overline{\mathrm{AB}}\) = 4.5 cm, \(\overline{\mathrm{BC}}\) = 5.5 cm. \(\overline{\mathrm{CD}}\) = 5 cm. ∠B = 60° and ∠C = 135°.

Solution:

Steps of Construction:

- Draw \(\overline{\mathrm{AB}}\) = 4.5 cm.
- Draw an angle of 60° at B and cut \(\overline{\mathrm{BC}}\) = 5.5 cm.
- Draw an angle of 135° at C and cut \(\overline{\mathrm{CD}}\) = 5 cm.
- Join \(\overline{\mathrm{AD}}\).
- □ABCD is the required quadrilateral.