1. One common misconception in developments of Geometry is that one can justify the fact that the slope of a line is well defined independent of the choice of points used to compute it through the use of silmilar triangles. In this development, similar triangles are practically the last topic, where we can show that the slope of a line is well defined as the first result using simply algebra. As a result, we have that similar triangles is very heavily dependent on the fact that the slope of a line is well defined, not the other way around.
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