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.
