**Construct parallelograms ABCD with the following measurements:**

**(a) AD = 4.2 cm, DC = 5.8 cm, ∟D = 43˚ **

**(b) AB = 43. Cm, BC = 3.2 CM, ∟C= 120˚**

**(c) AD =4.2 cm, DC = 5.8 cm, AC = 3.4cm **

**(d) AD = 4.3 cm, DC = 5.7 cm, DB = 7cm **

**(e) AD = 6.8 cm , DB = 7.6 cm, AD = 6.4cm **

**Solution: **

**(a) AD = 4.2cm, DC = 5.8cm, ∟D = 43˚**

Steps of construction:

- Draw a line segment AD = 4.2cm.
- Draw DC = 5.8cm such that ∠ADC = 43°
- With A as center and 5.8cm as radius draw another arc to intersect the above at B.
- Join AB and CB.

ABCD is the required parallelogram

**(b) AB = 43. Cm, BC = 3.2 CM, ∟C= 120˚**

Steps of construction:

C = 120 A =120 (opposite angles of a parallelogram)

BC = 3.2cm A = 3.2cm (opposite angles of a parallelogram)

- Draw a line segment AB = 4.3 cm.
- At A make an angle of 120° and draw AE.
- In A cut off AD = 3.2cm on AE.
- With B as center and 3.2cm as radius draw an arc.
- With D as center and 4.3 cm as radius draw another arc to intersect the above at C.
- Join BC and DC.

ABCD is the required parallelogram.

**(c) AD =4.2 cm, DC = 5.8 cm, AC = 3.4 cm **

Step of construction:

- Draw AD = 4.2cm
- With A as center and 3.4 cm as radius draw an arc.
- With D as center and 5.8cm as radius draw another arc to intersect the above arc
- Join AC and DC.
- With A as center and 5.8 cm radius draw an arc.
- With C as center and 4.2cm as radius draw another arc to intersect the above at B.
- Join AB and CB.

ABCD is the required parallelogram.

**(d) AD = 4.3 cm, DC = 5.7 cm, DB = 7cm **

AD = 4.3 cm DC = 5.7 cm = AB

Step of construction:

- Draw AD = 5.7cm
- With A as center and 4.3 cm as radius draw an arc.
- With B as center and 7cm as radius, draw another arc to intersect the above at D.
- Join AD and BD
- With B as center and 4.3 cm as radius draw an arc.
- With D as center and 5.7 cm as radius draw another arc to intersect the above at C.
- Join DC and BC.

ABCD is the required parallelogram

**(e) AD = 6.8cm , DB = 7.6cm, AD = 6.4cm **

Diagonals AC and BD bisect each other at E

AE = EC = ^{6.8}/_{2} = 34

AE = EC = ^{7.6}/_{2} = 3.8

Step of construction:

- Draw AD = 6.4cm.
- With A as center and 3.4 cm as radius draw an arc.
- With D as center and 3.8cm as radius draw another arc to intersect the above arc at E.
- Join AE and produce to C such that EC = 3.4cm.
- Join DE and produces to B such that EB = 3.8cm.
- Join AB, BC and DC.

ABCD is the required parallelogram

**Cons trust rectangle ABCD with the following data:**

**(a) AB = 4cm, BC = 6cm **

Step of construction:

- Draw AB = 4cm.
- Construct a perpendicular to AB at B and cut off BC = 6cm.
- With A as center and 6cm as radius draw an arc.
- With C as center and 4cm as radius draw another arc to intersect the above arc at D.
- Join AD and CD.

ABCD is the required parallelogram.

**(b) AB = 6cm , AC = 7.2 cm **

Step of construction:

- Draw AB = 6cm.
- At B construct ABE = 90.
- With A as center and 7.2 cm as radius draw an arc to intersect the above at C.
- Join AC.
- Construct BAF = 900.
- With B as center and 7.2 cm as radius draw an arc to intersect the above at D.
- Join CD.

ABCD is the required parallelogram.

**Construct square ABCD.****a) Which has side – length 2 cm****b) Which has diagonal 6cm**

**Solution: **

- a) Which has side – length 2 cm

Step of construction:

- Draw AB = 2cm
- At A draw AE AB
- With A as center and 2cm as radius draw an arc to intersect AE at D.
- With D as center and 2cm as radius draw an arc.
- With B as center and 2cm as radius draw another arc to intersect the above at C.
- Join BC and DC

ABCD is the required parallelogram.

**b) Which has diagonal 6cm**

Step of construction:

- Draw AC = 6cm.
- Draw the perpendicular bisecular of AC to intersect it at E.
- With E as center and 3 cm as radius draw an arc to intersect the above at B and D.
- Join AB, BC, CD, and DA.

ABCD is the required parallelogram.

- Construct rhombus ABCD such that:
- a) AB = 3.2 cm, AC =4.8 cm
- b) AB = 4.4 cm, BD = 5.4 cm
- c) AC = 7 cm, BD = 4 cm
- d) BD =6.8cm, AC = 5.4 cm.

Solution:

- a) AB = 3.2 cm, AC =4.8 cm

Step of construction:

- Draw AC = 3.2 cm.
- With A as center and 4.8 cm as radius draw an arc.
- With B as center and 3.2 cm as radius draw another arc to intersect to above at C.
- Join AC and BC.
- With A as center and 3.2 cm as radius draw an arc.
- With C as center and 3.2 cm as radius draw another arc to intersect the above at D.
- Join AD and CD.

ABCD is the required parallelogram.

**b) AB = 4.4 cm, BD = 5.4 cm.**

Step of construction:

- Draw a AB = 4.4 cm.
- With A as center and 4.4 cm as radius draw an arc.
- With B as center and 5.4 cm as radius draw another arc to intersect to above at D.
- Join AD and BD.
- With B as center and 4.4 cm radius draw an arc.
- With D as center and 4.4 cm as radius draw another arc to intersect the above at C.
- Join DC and BC.

ABCD is the required parallelogram.

**c) AC = 7cm, BD = 4 cm**

7cm

4cm E

Step of construction:

- Draw AC = 7 cm.
- Draw perpendicular bisector of AC to intersect or it at E.
- Cut off ED = EB = 2 cm.
- Join AB, BC, CD and DA.

- d)
**BD = 6.8 cm, AC = 5.4 cm**

Step of construction:

- Draw BD = 6.8 cm.
- Draw PQ the perpendicular bisector of BD to intersect or it at E.
- Cut off EA = EC = 2.7 cm.
- Join AB, BC, CD and DA.

ABCD is the required square.

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