A Full Axiomatic Development of High School Geometry

Preface
Acknowledgements
Contents
Foundational Principles
	Non-triviality and Betweenness
	Congruence and Length Measure
	Circles
	Triangle Congruence
	Upgrading Euclidean Constructions
Neutral Geometry
Similar Figures
	The Euclidean Parallel Axiom
	The Scaling Lemma
	The Scaling Theorem
	Similarity
Area Measure
	Polygonal Regions
	Decompositional Equivalence
	Polygonal Area
	The Area Measure Theorem
	Consequences of Area Measure
Angle Measure
	Ordering Angles
	Degree Measure
	Angle Measure and Congruence
	The Angle Measure Theorem
	Consequences of Angle Measure
Trigonometry
Circle Measure
	Jordan Measure of Area
	Inscribed Convex Polygons
	Circumscribed Convex Polygons
	Area, Circumference and the Number
Consistency and Models
	Birkhoff\'s Geometry
	Consistency
	Euclidean Fields
	Models from Euclidean Fields
	All Models
	The Constructible Plane
Appendix A: Axioms
Appendix B: MCL#9
Appendix C: Font Guide
Appendix D: Theorem Index
Appendix E: Notation Index
Bibliography
Index