Question

Construct a rhombus ABCD, if ;

(i) AB = 4 cm and $\angle \text{B}={120}^{\circ }$.

(ii) BC = 4.7 cm and $\angle \text{B}={75}^{\circ }$

(iii) CD = 5 cm and diagonal BD = 8.5 cm.

(iv) BC = 4.8 cm, and diagonal AC = 7 cm.

(v) diagonal AC = 6 cm and diagonal BD = 5.8 cm.

(vi) diagonal AC = 4.9 cm and diagonal BD = 6 cm.

(vii) diagonal AC = 6.6 cm and diagonal BD = 5.3 cm.

Answer 1

(i)

Steps : 1. Draw AB = 4 cm.

2. At B, draw $\angle \text{XBA}={120}^{\circ }$

3. Cut BC = 4 cm.

4. Draw arcs of radii 4 cm each from A and C which intersect at D.

Join CD and AD.

Thus ABCD is the required thombus.

(ii)

Steps :

1. Draw BC = 4.7 cm.

2. At B, draw $\angle \text{XBC}={75}^{\circ }$

3. Cut BA = 4.7 cm

4. From A and C, draw arcs of radii 4.7 cm each which intersect at D.

5. Join AD and CD.

Thus ABCD is the rhombus.

(iii)

Steps :

1. Draw CD = 5 cm.

2. From C & D draw arcs of radii 5 cm and 8.5 cm respectively which intersect at B.

3. From B and D, draw arcs of radii 5 cm each which intersect at A.

4. Join AB and AD.

Thus ABCD is the required rhombus.

(iv)

Steps : 1. Draw AC = 7 cm.

2. Draw arcs of radii 4.8 cm each from A and C which intersect at B.

3. From A & C again draw arcs of radii 4.8 cm each which intersect at D.

4. Join AB, BC, AD and CD.

Thus ABCD is the required rhombus.

(v)

Steps :

1.Draw BD = 5.8 cm.

2. Draw perpendicular bisector XY of BD.

3. Cut OA = OC = 3 cm (half the diagonal 6 cm)

4. Join AB, AD, BC and CD. Thus ABCD is the required rhombus.

(vi)

Steps :

1. Draw AC = 4.9 cm.

2. Draw perpendicular bisector XY of AC.

3. Cut OB = OD = 3 cm (half the diagonal 6 cm)

4. Join AB, BC, AD and CD.

Thus ABCD is the required rhombus.

(vii)

Steps : 1. Draw BD = 5.3 cm.

2. Draw perpendicular bisector XY of BD.

3. Cut OA = OC = 3.3 cm (half the diagonal 6.6 cm)

4. Join AB, AD, BC and CD.

Thus ABCD is the required rhombus.