Solving Problems In Geometry

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Front Cover Title Page PREFACE CONTENTS Chapter 1 PLANE GEOMETRY SEC. 1. METHODS OF SOLVING GEOMETRICAL PROBLEMS I. Triangles and Quadrilaterals II. Circles III. Areas of Plane Figures SEC. 2. TRIANGLES AND QUADRILATERALS PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE I. Right Triangles II. Isosceles Triangles III. Arbitrary Triangles IV, Parallelograms V. Trapezoids VI. Miscellaneous Problems SEC. 3. CIRCLES PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE I. Circles II. Inscribed and Circumscribed Triangles III. A Circle and a Triangle Arranged Arbitrarily IV. A Circle and a Quadrilateral V. Miscellaneous Problems SEC. 4. AREAS OF PLANE FIGURES PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE I. Area of Triangles II. Area of Quadrilaterals III. Area of Polygons IV. Area of Combined Figures V. Miscellaneous Problems SEC. 5. GEOMETRICAL TRANSFORMATIONS PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE I. Symmetry with Respect to a Point II. Symmetry About a Straight Line III. Rotation IV. Translation V. Homothetlc Transformation SEC. 6. VECTORS I. Affine Problems II. Metric Problems PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE I. Addition and Subtraction of Vectors.Multiplication of a Vector by a Number II. Scalar Product of Vectors III. Miscellaneous Problems SEC. 7. GREATEST AND LEAST VALUES PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE Chapter 2 SOLID GEOMETRY SEC. 8. CONSTRUCTING THE REPRESENTATION OF A GIVEN FIGURE SEC. 9. GEOMETRICAL CONSTRUCTIONS IN SPACE I. Simplest Constructions in Space II. Loci of Points III. Applications of Certain Loci of Points and Straight Lines IV. Constructions on Representations PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE I. Simplest Constructions in Space II. Loci of Points III. Applications of Certain Loci of Points and Lines IV. Constructions on Representations (1) Constructing Plane Figures in Space (2) Section of a Polyhedron by a Plane Parallel to Two Straight Lines (3) Cons tructing a Perpendicular to a Straight Line and a Perpendicular to a Plane (4) Section of a Polyhedron by a Plane PassingThrough a Given Point Perpendicular to a Given Line (5) Constructing a Locus of Points Equidistant from Given Points SEC. 10. SKEW LINES. ANGLE BETWEEN A STRAIGHT LINE AND A PLANE PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE SEC. 11. DIHEDRAL AND POLYHEDRAL ANGLES PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE SEC. 12. SECTIONS OF POLYHEDRONS PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE SEC. 13. SURFACES PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE SEC. 14. VOLUMES PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE SEC. 15. COMBINATIONS OF POLYHEDRONS AND CIRCULAR SOLIDS PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE SEC. 16. GREATEST AND LEAST VALUES PROBLEMS TO BE SOLVED WITHOUT ASSISTANCE! ANSWERS AND HINTS Chapter 1 Chapter 2 Back Cover