- Page 1: Foundations of GeometryLecture Note
- Page 4 and 5: ivCONTENTS30 Triangles in Neutral G
- Page 6 and 7: 2 SECTION 1. PREFACEare enrolled in
- Page 8 and 9: 4 SECTION 1. PREFACEre-learning it
- Page 10 and 11: 6 SECTION 2. NCTM3. To guide in the
- Page 12 and 13: 8 SECTION 2. NCTMTechnology. Techno
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- Page 16 and 17: 12 SECTION 3. CA STANDARDIn 2005 Ca
- Page 18 and 19: 14 SECTION 3. CA STANDARDThe Califo
- Page 20 and 21: 16 SECTION 3. CA STANDARDCalifornia
- Page 22 and 23: 18 SECTION 4. COMMON COREAt all lev
- Page 24 and 25: 20 SECTION 5. LOGIC AND PROOFour th
- Page 26 and 27: 22 SECTION 5. LOGIC AND PROOFRene D
- Page 28 and 29: 24 SECTION 5. LOGIC AND PROOF“I
- Page 30 and 31: 26 SECTION 6. REAL NUMBERSThe inter
- Page 34 and 35: 30 SECTION 7. EUCLID’S ELEMENTSEu
- Page 36 and 37: 32 SECTION 7. EUCLID’S ELEMENTSFi
- Page 38 and 39: 34 SECTION 8. HILBERT’S AXIOMSiom
- Page 40 and 41: 36 SECTION 8. HILBERT’S AXIOMS«
- Page 42 and 43: 38 SECTION 9. BIRKHOFF/MACLANE AXIO
- Page 44 and 45: 40 SECTION 9. BIRKHOFF/MACLANE AXIO
- Page 46 and 47: 42 SECTION 10. THE SMSG AXIOMSP is
- Page 48 and 49: 44 SECTION 10. THE SMSG AXIOMS« CC
- Page 50 and 51: 46 SECTION 11. THE UCSMP AXIOMSin s
- Page 52 and 53: 48 SECTION 11. THE UCSMP AXIOMS« C
- Page 54 and 55: 50 SECTION 12. VENEMA’S AXIOMS3.
- Page 56 and 57: 52 SECTION 12. VENEMA’S AXIOMS«
- Page 58 and 59: 54 SECTION 13. INCIDENCE GEOMETRYFi
- Page 60 and 61: 56 SECTION 13. INCIDENCE GEOMETRYEx
- Page 62 and 63: 58 SECTION 13. INCIDENCE GEOMETRYFi
- Page 64 and 65: 60 SECTION 13. INCIDENCE GEOMETRY«
- Page 66 and 67: 62 SECTION 14. BETWEENNESSFigure 14
- Page 68 and 69: 64 SECTION 14. BETWEENNESSTheorem 1
- Page 70 and 71: 66 SECTION 14. BETWEENNESS(a) To sh
- Page 72 and 73: 68 SECTION 14. BETWEENNESSThe follo
- Page 74 and 75: 70 SECTION 14. BETWEENNESSExample 1
- Page 76 and 77: 72 SECTION 14. BETWEENNESSorf(A) >
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- Page 80 and 81: 76 SECTION 15. THE PLANE SEPARATION
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78 SECTION 15. THE PLANE SEPARATION
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80 SECTION 16. ANGLESFigure 16.1: T
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82 SECTION 16. ANGLESCorollary 16.6
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84 SECTION 16. ANGLESFigure 16.6: I
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86 SECTION 16. ANGLESD cannot be in
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88 SECTION 17. THE CROSSBAR THEOREM
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90 SECTION 17. THE CROSSBAR THEOREM
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92 SECTION 18. LINEAR PAIRSFigure 1
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94 SECTION 18. LINEAR PAIRSγ + ∠
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96 SECTION 19. ANGLE BISECTORSwith
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98 SECTION 19. ANGLE BISECTORSAngle
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100 SECTION 20. THE CONTINUITY AXIO
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102 SECTION 20. THE CONTINUITY AXIO
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104 SECTION 21. SIDE-ANGLE-SIDEBirk
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106 SECTION 21. SIDE-ANGLE-SIDEFigu
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108 SECTION 22. NEUTRAL GEOMETRYEll
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110 SECTION 22. NEUTRAL GEOMETRY«
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112 SECTION 23. ANGLE-SIDE-ANGLEFig
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114 SECTION 23. ANGLE-SIDE-ANGLE«
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116 SECTION 24. EXTERIOR ANGLESTheo
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118 SECTION 24. EXTERIOR ANGLES« C
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120 SECTION 25. ANGLE-ANGLE-SIDEBy
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122 SECTION 26. SIDE-SIDE-SIDECase
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124 SECTION 26. SIDE-SIDE-SIDEBy si
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126 SECTION 27. SCALENE AND TRIANGL
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128 SECTION 27. SCALENE AND TRIANGL
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130 SECTION 28. CHARACTERIZATION OF
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132 SECTION 28. CHARACTERIZATION OF
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134 SECTION 29. TRANSVERSALSFigure
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136 SECTION 29. TRANSVERSALSCorolla
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138 SECTION 30. TRIANGLES IN NEUTRA
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140 SECTION 30. TRIANGLES IN NEUTRA
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142 SECTION 30. TRIANGLES IN NEUTRA
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144 SECTION 30. TRIANGLES IN NEUTRA
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146 SECTION 31. QUADRILATERALS IN N
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148 SECTION 31. QUADRILATERALS IN N
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150 SECTION 31. QUADRILATERALS IN N
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152 SECTION 31. QUADRILATERALS IN N
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154 SECTION 31. QUADRILATERALS IN N
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156 SECTION 32. THE EUCLIDEAN PARAL
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158 SECTION 32. THE EUCLIDEAN PARAL
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160 SECTION 32. THE EUCLIDEAN PARAL
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162 SECTION 32. THE EUCLIDEAN PARAL
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164 SECTION 32. THE EUCLIDEAN PARAL
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166 SECTION 32. THE EUCLIDEAN PARAL
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168 SECTION 33. RECTANGLESLemma 33.
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170 SECTION 33. RECTANGLESFigure 33
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172 SECTION 33. RECTANGLES« CC BY-
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174 SECTION 34. THE PARALLEL PROJEC
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176 SECTION 34. THE PARALLEL PROJEC
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178 SECTION 35. SIMILAR TRIANGLESBy
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180 SECTION 35. SIMILAR TRIANGLESCo
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182 SECTION 36. TRIANGLE CENTERSFig
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184 SECTION 36. TRIANGLE CENTERSThe
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186 SECTION 36. TRIANGLE CENTERSCen
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188 SECTION 37. AREADefinition 37.5
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190 SECTION 37. AREAToday’s Lesso
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192 SECTION 38. THE PYTHAGOREAN THE
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194 SECTION 38. THE PYTHAGOREAN THE
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196 SECTION 38. THE PYTHAGOREAN THE
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198 SECTION 38. THE PYTHAGOREAN THE
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200 SECTION 38. THE PYTHAGOREAN THE
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202 SECTION 39. CIRCLESFigure 39.1:
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204 SECTION 39. CIRCLESFigure 39.3:
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206 SECTION 39. CIRCLESFigure 39.5:
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208 SECTION 39. CIRCLESTheorem 39.1
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210 SECTION 39. CIRCLESLet D be the
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212 SECTION 39. CIRCLES« CC BY-NC-
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214 SECTION 40. CIRCLES AND TRIANGL
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216 SECTION 40. CIRCLES AND TRIANGL
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218 SECTION 40. CIRCLES AND TRIANGL
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220 SECTION 41. EUCLIDEAN CIRCLESFi
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222 SECTION 41. EUCLIDEAN CIRCLESFi
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224 SECTION 41. EUCLIDEAN CIRCLESFi
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226 SECTION 41. EUCLIDEAN CIRCLESFi
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228 SECTION 41. EUCLIDEAN CIRCLESBy
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230 SECTION 42. AREA AND CIRCUMFERE
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232 SECTION 42. AREA AND CIRCUMFERE
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234 SECTION 42. AREA AND CIRCUMFERE
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236 SECTION 42. AREA AND CIRCUMFERE
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238 SECTION 43. INDIANA BILL 246the
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240 SECTION 44. ESTIMATING πFigure
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242 SECTION 44. ESTIMATING πso tha
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244 SECTION 44. ESTIMATING πn π n
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246 SECTION 44. ESTIMATING πTable
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248 SECTION 44. ESTIMATING πnums =
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250 SECTION 44. ESTIMATING π« CC
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252 SECTION 45. EUCLIDEAN CONSTRUCT
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254 SECTION 45. EUCLIDEAN CONSTRUCT
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256 SECTION 45. EUCLIDEAN CONSTRUCT
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258 SECTION 45. EUCLIDEAN CONSTRUCT
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260 SECTION 45. EUCLIDEAN CONSTRUCT
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262 SECTION 45. EUCLIDEAN CONSTRUCT
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264 SECTION 46. HYPERBOLIC GEOMETRY
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266 SECTION 46. HYPERBOLIC GEOMETRY
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268 SECTION 46. HYPERBOLIC GEOMETRY
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270 SECTION 46. HYPERBOLIC GEOMETRY
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272SECTION 47.PERPENDICULAR LINES I
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274SECTION 47.PERPENDICULAR LINES I
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276 SECTION 48. PARALLEL LINES IN H
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278 SECTION 48. PARALLEL LINES IN H
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280 SECTION 48. PARALLEL LINES IN H
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282 SECTION 48. PARALLEL LINES IN H
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284 SECTION 49. TRIANGLES IN HYPERB
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286 SECTION 49. TRIANGLES IN HYPERB
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288 SECTION 49. TRIANGLES IN HYPERB
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290 SECTION 50. AREA IN HYPERBOLIC
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292 SECTION 50. AREA IN HYPERBOLIC
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294 SECTION 50. AREA IN HYPERBOLIC
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296 SECTION 50. AREA IN HYPERBOLIC
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298 SECTION 51. THE POINCARE DISK M
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300 SECTION 51. THE POINCARE DISK M
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302 SECTION 51. THE POINCARE DISK M
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304 SECTION 51. THE POINCARE DISK M
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306 SECTION 52. ARC LENGTHAs we see
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308 SECTION 52. ARC LENGTHProof. Su
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310 SECTION 52. ARC LENGTHThus the
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312 SECTION 52. ARC LENGTHMeasuring
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314 SECTION 53. SPHERICAL GEOMETRYW
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316 SECTION 53. SPHERICAL GEOMETRYF
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318 SECTION 53. SPHERICAL GEOMETRYP
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320 APPENDIX A. SYMBOLS USEDAppendi
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322 APPENDIX A. SYMBOLS USEDTechnol