### 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:

*: Draw a line segment \(DU\) \(=\) \(8\) \(cm\).*

**Step 1***: 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 2***: Join \(DC\) and \(UC\).*

**Step 3***: 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 4***: Join \(DK\) and \(CK\).*

**Step 5***: \(DUCK\) is the required parallelogram. The measure of \(KE\) gives the height of the parallelogram \(DUCK\).*

**Step 6**