Chapter 1 - Geometric Proofs
For many students, high school geometry is their first introduction to linear reasoning in the form of geometric proofs. On the one hand, this is a good thing because this is a big part of what real mathematics is about. On the other hand, it's a bad thing because it often becomes the point of the class, overtaking the actual geometry. Our Essential Geometry text has none of this material in it. That book focuses entirely on geometric concepts. This chapter in the advanced course takes a detailed look at mathematical reasoning and how it applies to geometric concepts.
Section 2.1 discusses the two basic types of reasoning and can be taught at any point during a standard geometry course. Section 2.2 requires only basic concepts such as congruence, perpendicularity and complementary vs. supplementary angles. Section 2.3 requires the same material as Section 2.2 with the addition of parallel lines. Section 2.4 adds an understanding of triangles and Section 2.5 brings in polygons including quadrilaterals.