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### 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 $$ABCD$$.