10. Constructing a parallelogram with two adjacent sides and one angle

Construct a parallelogram \(ABCD\) with \(AB\) \(=\) \(6\) \(cm\), \(BC\) \(=\) \(5.5\) \(cm\) and \(\angle ABC\) \(=\) \(75^{\circ}\).

 

Construction:

 

Step 1: Draw a line segment \(AB\) \(=\) \(6\) \(cm\).

 

Step 2: With \(B\) as centre, mark an angle \(75^{\circ}\) using the protractor and mark it as \(X\). Join \(BX\).

 

Step 3: With \(B\) as centre, draw an arc of radius \(5.5\) \(cm\) intersecting \(BX\) at \(C\).

 

Step 4: With \(C\) and \(A\) as centres, draw two arcs of radii \(6\) \(cm\) and \(5.5\) \(cm\) respectively such that they intersect each other at \(D\).

 

Step 5: Join \(CD\) and \(AD\).

 

Step 6: \(ABCD\) is the required parallelogram. The measure of \(CE\) gives the height of the parallelogram \(ABCD\).