The DAV Maths Class 8 Solutions and **DAV Class 8 Maths Chapter 12 Worksheet 2** Solutions of Construction of Quadrilaterals offer comprehensive answers to textbook questions.

## DAV Class 8 Maths Ch 12 WS 2 Solutions

Question 1.

Construct a quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 4 cm, \(\overline{\mathrm{BC}}\) = 3 cm, \(\overline{\mathrm{CD}}\) = 3.5 cm and diagonals are \(\overline{\mathrm{AC}}\) = 6 cm and \(\overline{\mathrm{BD}}\) = 5.5 cm.

Solution:

Steps of Construction:

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

2. Draw arcs from A and B with radii 6 cm and 3 cm respectively to meet at C.

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

4. Draw arcs from C and B with radii 3.5 cm and 5.5 cm respectively to meet at D.

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

6. ABCD is the required quadrilateral.

Question 2.

Construct a quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = \(\overline{\mathrm{BC}}\) = 5 cm, \(\overline{\mathrm{CD}}\) = 6 cm, diagonals are 7 cm each.

Solution:

Steps of Construction:

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

2. Draw arcs from A and B with radius 7 cm and 5 cm respectively.

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

4. Draw arcs from C and B with centres 6 cm and 7 cm respectively.

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

6. ABCD is the required quadrilateral.

Question 3.

Construct a quadrilateral ABCD in which three sides are 4 cm each and both diagonals are 6 cm each.

Solution:

Steps of Construction:

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

2. Draw arcs from A and B with radii 6 cm and 4 cm respectively to meet at C.

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

4. Draw arcs from C and B with radii 4 cm and 6 cm respectively to meet at D.

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

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

7. ABCD is the required quadrilateral.

Question 4.

Construct a quadrilateral MNRS with sides \(\overline{\mathrm{MN}}\) = 5.5 cm, \(\overline{\mathrm{NR}}\) = 6 cm, \(\overline{\mathrm{RS}}\) = 6.5 cm and diagonals \(\overline{\mathrm{MR}}\) = 8 cm and \(\overline{\mathrm{NS}}\) = 7.5 cm.

Solution:

Steps of Construction:

1. Draw \(\overline{\mathrm{MN}}\) = 5.5 cm.

2. Draw arcs from M and N with radii 8 cm and 6 cm respectively to meet at R.

3. Join \(\overline{\mathrm{MR}}\) and \(\overline{\mathrm{NR}}\).

4. Draw arcs from N and R with radii 7.5 cm and 6.5 cm respectively to meet at S.

5. Join \(\overline{\mathrm{NS}}\), \(\overline{\mathrm{RS}}\) and \(\overline{\mathrm{MS}}\).

6. MNRS is the required quadrilateral.

Question 5.

Construct a quadrilateral ABCD in which \(\overline{\mathrm{AB}}\) = 4.5 cm, \(\overline{\mathrm{BC}}\) = 4 cm, \(\overline{\mathrm{CD}}\) = 4.5 cm, diagonals \(\overline{\mathrm{AC}}\) = 6 cm and \(\overline{\mathrm{BD}}\) = 6.5 cm.

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 respectively to meet at C.

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

4. Draw arcs from B and C with radii 6.5 cm and 4.5 c respectively to meet at D.

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

6. ABCD is the required quadrilateral.

Question 6.

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

Solution:

Steps of Construction:

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

2. Draw arcs from A and B by taking a 6.5 cm radius for each.

3. Draw an arc from B by taking a 4 cm radius intersecting the previous arc at C.

4. Take a radius of 5 cm and draw an arc from C to intersect the previous arc at D.

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

6. ABCD is the required quadrilateral.