Reflections of a Point in the Midpoints of a Triangle's Sides
Let ABC be a triangle and P be an arbitrary point. Let A', B', and C' be symmetric to P with respect to the midpoints BC, CA, and AB, respectively. Then A'B'C' is congruent to ABC and their corresponding sides are parallel.
See problem 5.43 in V. Prasolov, Problems in Plane and Solid Geometry, Vol. 1, Plane Geometry [PDF], (D. Leites, ed. and trans.).