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1 Introduction
MAT 200
Course Notes on Geometry
Stony Brook Mathematics Department
Fall, 2002
1 Introduction
1.1 Physical vs. Ideal
1.2 The idea of constructibility
1.3 Basic objects
1.4 Basic concepts
1.5 Basic axioms
1.6 Basic notations
1.7 Basic constructions
2 Triangles and congruence of triangles
2.1 Basic measurements
2.2 Historical note
2.3 More on measurements
2.4 Congruence
2.5 Important remark about notation
2.6 The axiom for congruence
2.7 Exercises
2.8 Monotonicity of lengths and angles
2.9 Isosceles triangles
2.10 Congruence via
SSS
2.11 Inequalities for general triangles
2.12 Congruence via
AAS
2.13 Perpendicularity and orthogonality
3 The parallel axiom
3.1 Alternate interior angles
3.2 Existence of parallel lines
3.3 The sum of the angles of a triangle
4 Lengths, areas and proportions
4.1 Right triangles
4.2 Similar triangles
4.3 Basic trigonometric functions
4.4 Other important trigonometric formulae
5 Circles and lines
5.1 Circles
5.2 Central angles
5.3 Circumscribed circles
5.4 Tangent lines and inscribed circles
6 Some Amusements
6.1 Amusement 1:
6.2 Amusement 2:
6.3 Circles and circles
6.4 Orthogonal circles
6.5 Tangent circles
About this document ...
Scott Sutherland 2002-12-18