List of Figures

• Proposition
• Proposition
• Pasch's Triangle
• Crossbar Theorem
• Isosceles triangles
• Segment subtraction
• Theorem
• Angle subtraction
• Alternate interior angles
• Exterior angle theorem
• Side-Angle-Angle
• Segment midpoint
• Triangle inequality
• Saccheri-Legendre Theorem
• Right triangle with defect 0
• Rectangles
• Defect 0 for all right triangles
• Parallel lines in the Klein model
• Length in the Klein model
• Measuring angles in the Poincaré Half-Plane Model
• A p-line in the Poincaré disk model
• Angle measure in the Poincaré Disk Model
• Construction of the p-line through A and B
• Limiting Parallel Rays
• Hyperparallel Lines
• Horoparallel Lines
• Lambert Quadrilateral
• Saccheri Quadrilateral
• SAS in the Poincaré Model
• Angle of Parallelism
• Central Projection from N
• The Saccheri quadrilateral associated with
• A horocycle in the Poincaré model
• Concentric horocycles in the Poincaré model
• A hypercycle in the Poincaré model
• Horocyclic Sector in the Poincaré model
• Tractrix curve
• Graphs of hyperbolic functions
• Hyperbolic Circle
• Saccheri Quadrilateral
• Complementary Segments
• Engel's Theorem