5. Constructing a trapezium with three sides and a diagonal

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 $ABCD$.