- Browse
- » Geometry: includes plane, analytic, and transformational geometries
Geometry: includes plane, analytic, and transformational geometries
Author
Publisher
Varies, see individual formats and editions
Publication Date
Varies, see individual formats and editions
Language
English
More Details
Contributors
ISBN
9780071544122
9780071795401
9780071795401
Table of Contents
From the Book - 4th ed.
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.
Description
Loading Description...
Excerpt
Loading Excerpt...
Author Notes
Loading Author Notes...
Staff View
Loading Staff View.