That question has an answer: they crouched like birds. A 198 million year old fossil trackway from Utah has preserved a print of a theropod dinosaur taking a break, resting with hands curled inward and knuckle down, and legs bent. Except for the forelimbs, of course, it’s very birdlike.

Restoration of Early Jurassic environment preserved at the SGDS, with the theropod Dilophosaurus wetherilli in bird-like resting pose, demonstrating the manufacture of SGDS.18.T1 resting trace.
Here’s the section of the trace fossil they used to reconstruct the animal’s posture.

A, Overhead, slightly oblique angle photograph of SGDS.18.T1 resting trace. Note normal Eubrontes track cranial to resting traces (top center) made by track maker during first step upon getting up. Scale bar equals 10 cm. B, Schematic of SGDS.18.T1 to scale with A: first resting traces (manus, pes, and ischial callosity) in red, second (shuffling, pes only) traces in gold, final resting traces (pes and ischial callosity) in green, and tail drag marks made as track maker moved off in blue. Note long metatarsal (“heel”) impressions on pes prints. C, Direct overhead photograph and D, computerized photogrammetry with 5 mm contour lines of Eubrontes trace SGDS.18.T1. Color banding reflects topography (blue-green = lowest, purple-white = highest); a portion of the berm on which the track maker crouched is discernible. Abbreviations: ic = ischial callosity, lm = left manus, lp = left pes, rm = right manus, rp = right pes, td = tail drag marks.
Milner ARC, Harris JD, Lockley MG, Kirkland JI, Matthews NA (2009) Bird-Like Anatomy, Posture, and Behavior Revealed by an Early Jurassic Theropod Dinosaur Resting Trace. PLoS ONE 4(3): e4591. doi:10.1371/journal.pone.0004591




