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Construction of Parallelogram

Example 28: Construct a parallelogram MORE in which MO = 5.5 cm,
OR = 4.3 cm and diagonal MR = 8 cm.
Solution: Draw a rough sketch of the required parallelogram and write down
the given dimensions.
Steps of construction:
Step 1: Draw a line segment MO = 5.5 cm.
Step 2: With M as centre and radius 8.0 cm, draw an arc.

Step 3: With O as centre and radius 4.3 cm, draw another arc cutting
the previous arc at R.

Step 4: Join MR and OR.
Step 5: With M as centre and radius 4.3 cm, draw an arc.
Step 6: With R as centre and radius 5.5 cm, draw another arc cutting the previous drawn arc at E.

Step 7: Join EM and ER.
Thus, MORE is the required parallelogram.
Example 29: Draw a parallelogram ABCD given that BC = 4.5 cm, AC = 5.6 cm and BD = 4 cm.
Solution: We know that the diagonals of a parallelogram bisect each other.
First draw a rough sketch of the parallelogram as shown:
Steps of construction:

Step 1: Construct a DOBC with BC = 4.5 cm,
1  1 
BO = BD =  × 4 cm = 2 cm

2  2 
1  1 
and CO = AC =  × 56 .  cm = 2.8 cm
2  2 
Step 2: Produce BO to D, such that OD = OB.

Step 3: Produce CO to A, such that OA = OC.
Step 4: Join AB, DC and AD.
Thus, ABCD is the required parallelogram.
Example 30: Construct a parallelogram ABCD such that AC = 6 cm; BD = 4.8 cm and an angle
between them = 60°.
Solution: We know that the diagonals of a parallelogram bisect each other. Using this property of
parallelogram, we may proceed according to the given steps.
Steps of construction:

Step 1: Draw a line segment AC = 6 cm.
Step 2: Bisect AC at O.
Step 3: Draw ∠COX = 60° and produce XO to Y.

1 1
Step 4: Cut off OB = (4.8) cm = 2.4 cm and OD = (4.8) cm = 2.4 cm
2 2
Step 5: Join AB, BC, CD, DA.

Thus, ABCD is the required parallelogram.

79 Quadrilaterals