Problems in Geometry

Cover......Page 1
Title......Page 5
Copyright......Page 6
CONTENTS......Page 7
1. The Ratio and Proportionality of Line Segments, Similarity of Triangles......Page 9
2. Metric Relationships in a Right-Angled Triangle......Page 12
3. Regular Polygons, the Length of the Circumference and the Arc......Page 17
4. Areas of Plane Figures......Page 19
5. Solving Right-Angled Triangles......Page 24
Law of Cosines......Page 31
Law of Sines......Page 33
Areas of Triangles, Parallelograms and Quadrilaterals......Page 34
Particular Cases of Solving Oblique Triangles......Page 36
Heron's Formula......Page 37
Radii r and R of Inscribed and Circumscribed Circles and the Area S of a Triangle......Page 38
Miscellaneous Problems......Page 39
7. Basic Concepts and Axioms. Two Straight Lines in Space......Page 45
8. Straight Lines Perpendicular and Inclined to a Plane......Page 48
9. Angles Formed by a Straight Line and a Plane......Page 54
10. Parallelism of a Straight Line and a Plane......Page 57
11. Parallel Planes......Page 61
12. Dihedral Angles. Perpendicular Planes......Page 65
13. Areas of Projections of Plane Figures......Page 69
14. Polyhedral Projections......Page 71
15. Prisms and Parallelepipeds......Page 73
16. The Pyramid......Page 79
17. The Truncated Pyramid......Page 83
18. Regular Polyhedrons......Page 86
19. The Right Circular Cylinder......Page 88
20. The Right Circular Cone......Page 91
21. The Truncated Cone......Page 95
22. Areas of Parallelepipeds and Prisms......Page 99
23. Areas of Pyramids......Page 104
24. Areas of Truncated Pyramids......Page 107
25. Areas of Cylinders......Page 110
26. Areas of Cones......Page 113
27. Areas of Truncated Cones......Page 117
28. Volumes of Parallelepipeds......Page 120
29. Volumes of Prisms......Page 124
30. Volumes of Pyramids......Page 129
31. Volumes of Truncated Pyramids......Page 135
32. Volumes of Cylinders......Page 139
33. Volumes of Cones......Page 143
34. Volumes of Truncated Cones......Page 147
35. Spheres......Page 151
36. Areas of Spheres and Their Parts......Page 154
37. Volumes of Spheres and Their Parts......Page 157
38. Inscribed and Circumscribed Spheres......Page 161
39. Polyhedrons......Page 166
40. Round Solids......Page 170
41. Areas and Volumes of Prisms......Page 174
42. Areas and Volumes of Pyramids......Page 178
43. Areas and Volumes of Round Solids......Page 183
Answers......Page 189