Topic in geometry

Question 2 (24 marks) Let G = {T(z) = az + b +c: a,b,c C, |a| # 161}. 1. Show that (C,G) is a geometry in the sense of Felix Klein. 2. Show that every T E G sends straight lines to straight lines. 3. Show that all triangles in the complex plane are congruent in the geometry (C,G) 4. Show that the ratio of areas is invariant in the geometry (C,G)