In this paper we obtain the explicit forms of the covariogram and the orientation-dependent chord length distribution function for any parallelogram. The explicit form of the chord length distribution function for a parallelogram is also obtained.

The paper considers the problem of recognition of triangles by orientation-dependent chord length distribution. The following results are obtained: 1. The explicit form of the covariogram and orientation-dependent chord length distribution function for a triangle. 2. The explicit form for the chord length distribution function for a triangle. 3. The length of the maximal chord of a triangle is continuous function on direction. 4. If we have orientation-dependent chord length distribution function for an everywhere dense set, then we can uniquely recognize the triangle with respect to reflections and translations. 5. For any finite subset A, there are two non-congruent triangles with the same values of orientation dependent chord length distribution functions on A.