This study examined the extent to which haptic perception of two-dimensional (2-D) shape is modified by the design of the perceptual task (single-interval categorization vs. two-interval discrimination), the orientation of the angles in space (oblique vs. horizontal), and the exploration strategy (one or two passes over the angle). Subjects (n = 12) explored 2-D angles using the index finger of the outstretched arm. In the categorization task, subjects scanned individual angles, categorizing each as "large" or "small" (2 angles presented in each block of trials; range 80° vs. 100° to 89° vs. 91°; implicit standard 90°). In the discrimination task, a pair of angles was scanned (standard 90°; comparison 91-103°) and subjects identified the larger angle. The threshold for 2-D angle categorization was significantly lower than for 2-D angle discrimination, 4° versus 7.2°. Performance in the categorization task did not vary with either the orientation of the angles (horizontal vs. oblique, 3.9° vs. 4°) or the number of passes over the angle (1 vs. 2 passes, 3.9° vs. 4°). We suggest that the lower threshold with angle categorization likely reflects the reduced cognitive demands of this task. We found no evidence for a haptic oblique effect (higher threshold with oblique angles), likely reflecting the presence of an explicit external frame of reference formed by the intersection of the two bars forming the 2-D angles. Although one-interval haptic categorization is a more sensitive method for assessing 2-D haptic angle perception, perceptual invariances for exploratory strategy and angle orientation were, nevertheless, task-independent.