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Definitions and Theorems (Kay): You need to know the following definitions and theorems from Kay, from the second half of the material. Although the focus is on the second half, the material builds on the previous – you still need to know the definitions and main results from the first half of the course, particularly the major theorems from absolute geometry that appeared in chapter 3. The new material picks up at section 3.7 (quadrilaterals). Definitions and theorems below are in the order covered in class (and not necessarily the order in Kay). Definitions quadrilateral terminology (p 183) Axioms/Theorems properties of convex quadrilaterals (p 183) convex (p 183; defined precisely in lecture) congruence theorems for convex quadrilaterals – SASAS, ASASA, etc (pp 184185) rectangle (p 186) “theorem 2” and the other properties of Saccheri quadrilaterals on p 187 Saccheri quadrilateral (p186) Lambert quadrilateral (p 187) circle terminology (p 194) the circle properties on p 195 arc terminology (p 196) additivity of arc measure (p 197) tangent and secant (circles) (p 198) the tangent theorem (p 198) and its corollary (p 199) the possible cases for parallel lines (pp 425 426) Know which case defines spherical, which hyperbolic, and which Euclidean geometry the equivalent forms of Euclid’s Fifth, given on page 427 defect in hyperbolic geometry (p 438) hyperbolic parallel postulate (p 436) area in hyperbolic geometry (p 438) unnamed hyperbolic theorem 1 and its corollary on p 437 Poincaré disk model components (p 446) parallel (lines) (p 211) parallelism in absolute geometry (p 212) and equivalent forms for corresponding, same side interior, etc. Euclid’s Fifth Postulate (p 213) and equivalent forms for corresponding, same side interior, etc. Euclidean Parallel Postulate as stated as axiom P-1 in Kay (p 214) (unnamed) theorem 2 on p214, which is the same as Euclid’s Fifth transversal theorems (shorthand: C, F, and Z properties) (p 215) Euclidean exterior angle theorem (p 217) midpoint connector theorem (p 218) parallelogram, rhombus, square (p 224) (unnamed) theorem 1, and the properties of parallelograms on p 225 trapezoid (p 226) midpoint connector theorem for trapezoids (p 218) side-splitting theorem (p 229) (more circle/arc material) inscribed angle theorem (p 270) and corollaries on pp 272-273 two chord theorem (p 273) secant-tangent theorem (p 273) two secant theorem (p 273) regular polygon terminology (p 254) angle sum of convex n-gon (theorem 2) (p 255) Euclidean area axioms (1-6) (pp 286-287), and particularly Cavalieri’s Principle similar (polygons, esp. triangles) (p 236) AA, SAS, and SSS similarity criteria for triangles (pp 238-239) Note: material on polyhedral and volume mostly not from Kay. See also the sheets on “Formulas and computations” and “General stuff you should know.