We describe randomized parallel CREW PRAM algorithms for building trapezoidal diagrams of line segments in the plane. For general segments, we give an algorithm requiring optimal O(A + nlogn) expected work and optimal O(logn) time, where A is the number of intersecting pairs of segments. If the segments form a simple chain, we give an algorithm requiring optimal O(n) expected work and O(log n log log ra log∗ n) expected time, and a simpler algorithm requiring O(n log∗ n) expected work. The serial algorithm corresponding to the latter is the simplest known algorithm requiring O(n log∗ n) expected operations. For a set of segments forming K chains, we give an algorithm requiring O(A + n log∗ n + K log n) expected work and O(log n log log n log∗ n) expected time. The parallel time bounds require the assumption that enough processors are available, with processor allocations every log n steps.