### 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:

*: Draw a line segment \(AB\) \(=\) \(9\) \(cm\).*

**Step 1***: 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 2***: Join \(AC\) and \(BC\).*

**Step 3***: Draw a line \(CX\) parallel to \(AB\).*

**Step 4***: With \(C\) as centre, draw an arc of radius \(8\) \(cm\) intersecting \(CX\) at \(D\).*

**Step 5***: Join \(AD\). The measure of \(DE\) gives the height of the trapezium \(ABCD\).*

**Step 6**