Geometry : includes plane, analytic, and transformational geometries / Barnett Rich, Christopher Thomas.

includes index.

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.