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Theory:

Working rule to construct a parallelogram:
 
Let us discuss the working rule to construct a parallelogram when the measures of two adjacent sides and a diagonal of a parallelogram are given.
Example:
Construct a parallelogram \(DUCK\) with \(DU\) \(=\) \(8\) \(cm\), \(UC\) \(=\) \(6.5\) \(cm\) and \(DC\) \(=\) \(11\) \(cm\).
 
Construction:
 
Step 1: Draw a line segment \(DU\) \(=\) \(8\) \(cm\).
 
Step 2: With \(D\) and \(U\) as centres, draw two arcs of radii \(11\) \(cm\) and \(6.5\) \(cm\) respectively such that they intersect each other at \(C\).
 
Step 3: Join \(DC\) and \(UC\).
 
Step 4: With \(C\) and \(D\) as centres, draw two arcs of radii \(8\) \(cm\) and \(6.5\) \(cm\) respectively such that they intersect each other at \(K\).
 
Step 5: Join \(DK\) and \(CK\).
 
Step 6: \(DUCK\) is the required parallelogram. The measure of \(KE\) gives the height of the parallelogram \(DUCK\).
 
P - Case 2 GIF.gif