Problems in Geometry

Contents......Page 5 1. The Ratio and Proportionality of Line Segments, Similarity of Triangles......Page 7 2. Metric Relationships in a Right-Angled Triangle......Page 10 3. Regular Polygons, the Length of the Circumference and the Arc......Page 15 4. Areas of Plane Figures......Page 17 5. Solving Right-Angled Triangles......Page 22 Law of Cosines......Page 29 Law of Sines......Page 31 Areas of Triangles, Parallelograms and Quadrilaterals......Page 32 Particular Cases of Solving Oblique Triangles......Page 34 Heron's Formula......Page 35 Radii r and R of Inscribed and Circumscribed Circles and the Area S of a Triangle......Page 36 Miscellaneous Problems......Page 37 7. Basic Concepts and Axioms. Two Straight Lines in Space......Page 43 8. Straight Lines Perpendicular and Inclined to a Plane......Page 46 9. Angles Formed by a Straight Line and a Plane......Page 52 10. Parallelism of a Straight Line and a Plane......Page 55 11. Parallel Planes......Page 59 12. Dihedral Angles. Perpendicular Planes......Page 63 13. Areas of Projections of Plane Figures......Page 67 14. Polyhedral Angles......Page 69 15. Prisms and Parallelepipeds......Page 71 16. The Pyramid......Page 77 17. The Truncated Pyramid......Page 81 18. Regular Polyhedrons......Page 84 19. The Right Circular Cylinder......Page 86 20. The Right Circular Cone......Page 89 21. The Truncated Cone......Page 93 22. Areas of Parallelepipeds and Prisms......Page 97 23. Areas of Pyramids......Page 102 24. Areas of Truncated Pyramids......Page 105 25. Areas of Cylinders......Page 108 26. Areas of Cones......Page 111 27. Areas of Truncated Cones......Page 115 28. Volumes of Parallelepipeds......Page 118 29. Volumes of Prisms......Page 122 30. Volumes of Pyramids......Page 127 31. Volumes of Truncated Pyramids......Page 133 32. Volumes of Cylinders......Page 137 33. Volumes of Cones......Page 141 34. Volumes of Truncated Cones......Page 145 35. Spheres......Page 149 36. Areas of Spheres and Their Parts......Page 152 37. Volumes of Spheres and Their Parts......Page 155 38. Inscribed and Circumscribed Spheres......Page 159 39. Polyhedrons......Page 164 40. Round Solids......Page 168 41. Areas and Volumes of Prisms......Page 172 42. Areas and Volumes of Pyramids......Page 176 43. Areas and Volumes of Round Solids......Page 181 Answers......Page 187