11. Constructing a parallelogram with two adjacent sides and one diagonal

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 \(DUCK\).