Let P Denote The Set Of Points For A Hilbert Plane Suppose That F P P Is An Is

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

 

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