Geometry : includes plane, analytic, and transformational geometries

ch . 1. Lines, angles, and triangles -- 1.1. Historical background of geometry -- 1.2. Undefined terms of geometry : point, line, and plane -- 1.3. Line segments -- 1.4. Circles -- 1.5. Angles -- 1.6. Triangles -- 1.7. Pairs of angles -- ch. 2. Methods of proof -- 2.1. Proof by deductive reasoning -- 2.2. Postulates (assumptions) -- 2.3. Basic angle theorems -- 2.4. Determining the hypothesis and conclusion -- 2.5. Proving a theorem -- ch. 3. Congruent triangles -- 3.1. Congruent triangles -- 3.2. Isosceles and equilateral triangles -- ch. 4. Parallel lines, distances, and angle sums -- 4.1. parallel lines -- 4.2. Distances -- 4.3. Sum of the measures of the angles of a triangle -- 4.4. Sum of the measures of the angles of a polygon -- 4.5. Two new congruency theorems -- ch. 5. Parallelograms, trapezoids, medians, and midpoints -- 5.1. Trapezoids -- 5.2. Parallelograms -- 5.3. Special parallelograms : rectangle, rhombus, and square -- 5.4. Three or more parallels ; medians and midpoints -- ch. 6. Circles -- 6.1. The circle ; circle relationships -- 6.2. Tangents -- 6.3. Measurement of angles and arcs in a circle -- ch. 7. Similarity -- 7.1. Ratios -- 7.2. Proportions -- 7.3. Proportional segments -- 7.4. Similar triangles -- 7.8. Mean proportionals in a right triangle -- 7.9. Pythagorean theorem -- 7.10. Special right triangles -- ch. 8. Trigonometry -- 8.1. Trigonometric ratios -- 8.2. Angles of elevation and depression -- ch. 9. Areas -- 9.1. Area of a rectangle and of a square -- 9.2. Area of a parallelogram -- 9.3. Area of a triangle -- 9.4. Area of a trapezoid -- 9.5. Area of a rhombus -- 9.6. Polygons of the same size or shape -- 9.7. Comparing areas of similar polygons -- ch. 10. Regular polygons and the circle -- 10.1. Regular polygons -- 10.2. Relationships of segments in regular polygons of 3, 4, and 6 sides -- 10.3. Area of a regular polygon -- 10.4. Ratios of segments and areas of regular polygons -- 10.5. Circumference and area of a circle -- 10.6. Length of an arc ; area of a sector and a segment -- 10.7. Areas of combination figures -- ch. 11. Locus -- 11.1. Determining a locus -- 11.2. Locating points by means of intersecting loci -- 11.3. Proving a locus -- ch. 12. Analytic geometry -- 12.1. Graphs -- 12.2. Midpoint of a segment -- 12.3. Distance between two points -- 12.4. Slope of a line -- 12.5. Locus in analytic geometry -- 12.6. Areas in analytic geometry -- 12.7. Proving theorems with analytic geometry -- ch. 13. Inequalities and indirect reasoning -- 13.1. Inequalities -- 13.2. Indirect reasoning -- ch. 14. Improvement of reasoning -- 14.1. Definitions -- 14.2. Deductive reasoning in geometry -- 14.3. Converse, inverse, and contrapositive of a statement -- 14.4. Partial converse and partial inverse of a theorem -- 14.5. Necessary and sufficient conditions -- ch. 15. Constructions -- 15.1. Introduction -- 15.2. Duplicating segments and angles -- 15.3. Constructing bisectors and perpendiculars -- 15.4. Constructing a triangle -- 15.5. Constructing parallel lines -- 15.6. Circle constructions -- 15.7. Inscribing and circumscribing regular polygons -- 15.8. Constructing similar triangles -- ch. 16. Proofs of important theorems -- 16.1. Introduction -- 16.2. The proofs -- ch. 17. Extending plane geometry into solid geometry -- 17.1. Solids -- 17.2. Extensions to solid geometry -- 17.3. Areas of solids : square measure -- 17.4. Volumes of solids : cubic measure -- ch. 18. Transformations -- 18.1. Introduction to transformations -- 18.2. Transformation notation -- 18.3. Translations -- 18.4. Reflections -- 18.5. Rotations -- 18.6. Rigid motions -- 18.7. Dihilations -- ch. 19. Non-Euclidean geometry -- 19.1. The foundations of geometry -- 19.2. The postulates of Euclidean geometry -- 19.3. The fifth postulate problem -- 19.4. Different geometries -- Formulas for references -- Answers to supplementary problems -- Index.Geometry, Schaum's outlines geometry