Preface |
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xi | |
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1 | (9) |
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2 | (1) |
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3 | (2) |
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5 | (3) |
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8 | (2) |
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2 Axioms: From Euclid to Today |
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10 | (20) |
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10 | (4) |
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2.1.1 Components of an axiomatic system |
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11 | (1) |
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12 | (2) |
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2.2 Euclidean and Non-Euclidean Geometries |
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14 | (5) |
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2.2.1 Euclid's axiomatic system |
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14 | (1) |
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2.2.2 Non-Euclidean geometries |
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15 | (2) |
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2.2.3 More on Euclid's "Elements" |
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17 | (2) |
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19 | (1) |
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19 | (1) |
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20 | (1) |
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20 | (6) |
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26 | (1) |
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27 | (3) |
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30 | (41) |
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30 | (8) |
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3.1.1 Segments, angles, and polygons |
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30 | (3) |
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3.1.2 Similarity and congruence |
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33 | (2) |
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3.1.3 Special angles and parallel lines |
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35 | (3) |
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38 | (24) |
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3.2.1 Angle relations in polygons |
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39 | (3) |
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3.2.2 Congruence of triangles |
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42 | (1) |
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3.2.3 Median, bisector, and altitude |
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43 | (1) |
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3.2.4 Isosceles triangles |
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44 | (2) |
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3.2.5 Basic triangle inequalities |
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46 | (1) |
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3.2.6 Similarity of triangles |
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47 | (7) |
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54 | (1) |
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54 | (4) |
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58 | (3) |
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3.2.10 Supplemental Problems |
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61 | (1) |
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3.3 Parallelograms and Trapezoids |
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62 | (9) |
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62 | (3) |
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65 | (2) |
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67 | (1) |
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3.3.4 Supplemental Problems |
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68 | (3) |
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71 | (33) |
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4.1 Definitions and Properties |
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71 | (12) |
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83 | (8) |
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4.3 Lengths of Tangents and Chords |
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91 | (1) |
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4.4 Incircle and Circumcircle |
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92 | (6) |
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98 | (3) |
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4.6 Supplemental Problems |
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101 | (3) |
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104 | (27) |
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5.1 Area of a Polygonal Region |
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105 | (7) |
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5.2 Area and Circumference of a Circle |
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112 | (6) |
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5.2.1 A first approach to area |
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113 | (1) |
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5.2.2 A second approach to area |
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113 | (2) |
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5.2.3 Circumference of a circle |
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115 | (3) |
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5.3 Wallace-Bolyai-Gerwien Theorem |
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118 | (6) |
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124 | (5) |
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5.5 Supplemental Problems |
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129 | (2) |
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131 | (30) |
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131 | (4) |
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135 | (16) |
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135 | (4) |
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139 | (5) |
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144 | (3) |
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6.2.4 History and comments |
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147 | (4) |
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6.3 Reflection Properties and Applications |
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151 | (4) |
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155 | (3) |
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6.5 Supplemental Problems |
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158 | (3) |
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161 | (29) |
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161 | (3) |
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7.2 Definitions and Properties |
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164 | (7) |
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7.3 Unit Circle Trigonometry |
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171 | (2) |
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7.4 Summary of Identities |
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173 | (5) |
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178 | (6) |
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184 | (3) |
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7.7 Supplemental Problems |
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187 | (3) |
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190 | (30) |
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191 | (1) |
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192 | (4) |
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196 | (5) |
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201 | (6) |
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8.5 Systems of Equations, Revisited |
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207 | (4) |
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211 | (5) |
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216 | (2) |
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8.8 Supplemental Problems |
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218 | (2) |
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220 | (32) |
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221 | (4) |
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225 | (6) |
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231 | (5) |
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9.4 A Unified Definition of Conies as Loci |
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236 | (1) |
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9.5 Change of Coordinates |
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237 | (5) |
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9.6 The Graph of Ax2 + Bxy + Cy2 + Fx + Gy + H = 0 |
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242 | (5) |
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247 | (2) |
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9.8 Supplemental Problems |
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249 | (3) |
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252 | (24) |
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253 | (3) |
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10.2 Geometric Interpretation |
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256 | (7) |
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263 | (8) |
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271 | (2) |
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10.5 Supplemental Problems |
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273 | (3) |
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276 | (27) |
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276 | (1) |
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277 | (7) |
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11.3 Applications to Geometry |
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284 | (5) |
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289 | (7) |
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11.5 Applications of the Dot Product |
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296 | (3) |
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299 | (2) |
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11.7 Supplemental Problems |
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301 | (2) |
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12 Affine Transformations |
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303 | (27) |
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303 | (3) |
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306 | (7) |
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313 | (6) |
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319 | (3) |
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12.5 Affine Transformations of Conic Sections |
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322 | (3) |
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325 | (2) |
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12.7 Supplemental Problems |
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327 | (3) |
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330 | (24) |
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331 | (1) |
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332 | (4) |
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336 | (4) |
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13.4 Classical Applications |
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340 | (9) |
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349 | (3) |
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13.6 Supplemental Problems |
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352 | (2) |
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14 Coordinate Method with Software |
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354 | (191) |
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359 | (2) |
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361 | (1) |
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361 | (2) |
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Parallelograms and Trapezoids |
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363 | (1) |
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364 | (2) |
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366 | (3) |
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369 | (1) |
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370 | (1) |
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371 | (1) |
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372 | (1) |
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373 | (1) |
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374 | (1) |
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375 | (1) |
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376 | (2) |
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Solutions to Chapter Problems |
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378 | (1) |
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378 | (1) |
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Axioms: From Euclid to Today |
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379 | (6) |
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385 | (16) |
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Parallelograms and Trapezoids |
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401 | (9) |
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410 | (21) |
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431 | (20) |
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451 | (14) |
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465 | (16) |
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481 | (11) |
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492 | (14) |
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506 | (11) |
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517 | (9) |
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526 | (8) |
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534 | (11) |
Bibliography |
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545 | (4) |
Index |
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549 | (6) |
About the Authors |
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555 | |