Theory:

Working rule to construct a trapezium:
 
Let us discuss the working rule to construct a trapezium when the measure of three sides and one diagonal of a trapezium are given.
Example:
Construct a trapezium \(ABCD\) in which \(\overline{AB}\) is parallel to \(\overline{CD}\), \(AB\) \(=\) \(9\) \(cm\), \(BC\) \(=\) \(8\) \(cm\), \(CD\) \(=\) \(8\) \(cm\) and \(AC\) \(=\) \(13\) \(cm\).
 
Construction:
 
Step 1: Draw a line segment \(AB\) \(=\) \(9\) \(cm\).
 
Step 2: With \(A\) and \(B\) as centres, draw two arcs of radii \(13\) \(cm\) and \(8\) \(cm\) respectively such that they intersect each other at \(C\).
 
Step 3: Join \(AC\) and \(BC\).
 
Step 4: Draw a line \(CX\) parallel to \(AB\).
 
Step 5: With \(C\) as centre, draw an arc of radius \(8\) \(cm\) intersecting \(CX\) at \(D\).
 
Step 6: Join \(AD\). The measure of \(DE\) gives the height of the trapezium \(ABCD\).
 
T - case 1 GIF.gif