| Contents: |
What is geometry? Why should I take it? -- 1. The basics : undefined words, some defined words, axioms, and postulates -- 2. The beginnings of proofs -- 3. Improvement of reasoning : statement, converse, inverse, contrapositive ; necessary and sufficient conditions ; if and only if -- 4. Parallel lines, forever together -- 5. Mostly triangles -- 6. Secrets of proving congruent triangles -- 7. Similar figures and Pythagoras lives!!!! -- 8. Quadrilaterals squarely done -- 9. Interior and exterior angles -- 10. Areal search and securing the perimeter -- 11. Volumes and surface area -- 12. Circle I -- 13. Lines (the straight kind) and parabolas I (not straight) -- 14. Distance formula, midpoint formula, Circle II, and analytic geometry proofs -- 15. Functions, translations, stretches, contractions, flips -- 16. Parabolas II, ellipses, hyperbolas -- 17. Right and not so right-angle trig, law of sines, law of cosines -- 18. Constructions -- 19. Indirect proofs ; disproving by counterexample ; too much, just enough, or not enough -- 20. Miscellaneous : locus ; parallel lines ; larger and smaller sides and angles -- 21. Twenty-first-century SAT spin on geometry -- 22. Always-sometimes-never questions -- 23. Answers : you should always draw the picture if you are having problems -- Appendix : a radical chapter -- Index -- Acknowledgments -- About Bob Miller--in his own words. |
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