Construct a trapezoid given the length of each side.
My solution is below. I request verification, critique, improvements, or alternative approaches.
Solution: Let the parallel sides have lengths $b_1, b_2$ and the non-parallel sides $s_1, s_2$. Let $d = |b_1 - b_2|$.
Construct $\triangle ADX$ so that $AD = s_1, AX = s_2, DX = d$. Extend $DX$ to $C$ so that $DC = b_1$. Draw $AB$ with length $b_2$ parallel to $DC$. To show that $ABCD$ is the desired trapezoid, it is sufficient to show that $AX \cong BC$.
Observe that $ABCX$ is a parallelogram since $AB \cong XC$ and $AB \parallel XC$. Therefore $AX \cong BC$, completing the proof.