Let P denote the set of points for a Hilbert plane. Suppose that f : P – P is an isometry of this plane.

Let P denote the set of points for a Hilbert plane. Suppose that f : P -> P is an isometry ofthis plane. Recall that by definition, this means that for all points A and B in P, the segments ABand f(A)f(B) are congruent. Show that the isometry f also preserves angles: i.e. if A, B, and Care any three non-collinear points, and if D = f(A),E = f(B), F = f(C), then angle ABC is congruent to angle DEF.(Hint: Use triangle congruences