In this post, we will see the book  Solving Problems in Geometry byV. Gusev, V. Litvinenko, A. Mordkovich.This book is intended for students at pedagogical (teacher training) institutes majoring in mathematics or in mathematics and physics. It has been written in correspondence with the current syllabus "Solving Problems".When preparing the text, we wanted to represent the main types ofproblems in geometry found at school. The book contains about 1000problems that should be solved independently. Alongside rather simple problems, there are problems whose solution requires profound meditation and sometimes even a non standard approach. The solution of most of the problems in this book will help the student form the professional habits important for a future teacher of mathematics, that is, to know how to solve the geometrical problems covered by the mathematics syllabus for high schools and vocational schools.This book was translated from the Russian by Leonid Levant. The book was published by first Mir Publishers in 1988.Table of ContentsPreface 5Chapter 1. PLANE GEOMETRY 10Sec. 1. Methods of Solving Geometrical Problems 10I. Triangles and Quadrilaterals 10II. Circles 12III. Areas of Plane Figures 13Sec. 2. Triangles and Quadrilaterals 22Problems to Be Solved Without Assistance 28I. Right Triangles (1-12) 28II. Isosceles Triangles (13-31) 29III, Arbitrary Triangles (32-59) 30IV, Parallelograms (60-73) 31V. Trapezoids (74-92) 32VI, Miscellaneous Problems (93-110) 33Sec. 3. Circles 34Problems to Be Solved Without Assistance 40I. Circles (111-129) 40II. Inscribed and Circumscribed Triangles (130-157) 41III. A Circle and a Triangle Arranged Arbitrarily (158-175) 43IV, A Circle and a Quadrilateral (176-191) 44V, Miscellaneous Problems (192-219) 45Sec. 4, Areas of Plane Figures 47Problems to Be Solved Without Assistance 57I. Area of Triangles (220-247) 57II. Area of Quadrilaterals (248-271) 59III. Area of Polygons (272-279) 60IV. Area of Combined Figures (280-295) 61V, Miscellaneous Problems (296-321) 62Sec. 5. Geometrical Transformations 64Problems to Be Solved Without Assistance 68I. Symmetry with Respect to a Point (322-337) 68II. Symmetry About a Straight Line (338-362) 69III. Rotation (363-377) 70IV. Translation (378-390) 71V. Homothetic Transformation (391-397) 72Sec. 6. Vectors 73I. Affine Problems 75II. Metric Problems 81Problems to Be Solved Without Assistance 83I. Addition and Subtraction of Vectors, Multiplication of a Vectorby a Number (398-436) 83II. Scalar Product of Vectors (437-457) 86III. Miscellaneous Problems (458-534) 87Sec. 7. Greatest and Least Values 92Problems to Be Solved Without Assistance (535-562) 101Chapter 2. SOLID GEOMETRY 103Sec. 8. Constructing the Representation of a Given Figure 1 H3Sec. 9. Geometrical Constructions in Space 114I. Simplest Constructions in Space 114II. Loci of Points 115III. Applications of Certain Loci of Points and Straight Lines 117IV. Constructions on Representations 118Problems to Be Solved Without Assistance 126I, Simplest Constructions in Space (563-569) 126II. Loci of Points (570-583) 126III. Applications of Certain Loci of Points and Lines (584-592) 127IV. Constructions on Representations 127(1) Constructing Plane Figures in Space (593-597) 127(2) Section of a Polyhedron by a Plane Parallel to Two StraightLines (598-607) 127(3) Constructing a Perpendicular to a Straight Line and aPerpendicular to a Plane (608-617) 128(4) Section of a Polyhedron by a Plane Passing Through a GivenPoint Perpendicular to a Given Line (618-621) 129(5) Constructing a Locus of Points Equidistant from Given Points(622-630) 129Sec. 10. Skew Lines. Angle Between a Straight Line and a Plane 130Problems to Be Solved Without Assistance (631-689) 130Sec. 11. Dihedral and Polyhedral Angles 143Problems to Be Solved Without Assistance (690-723) 140Sec. 12. Sections of Polyhedrons 148Problems to Be Solved Without Assistance (724-762) 159Sec. 13. Surfaces 162Problems to Be Solved Without Assistance (763-799) 170Sec. 14. Volumes 172Problems to Be Solved Without Assistance (800-852) 17aSec. 15. Combinations of Polyhedrons and Circular Solids 183Problems to Be Solved Without Assistance (853-919) 1S9Sec. 16. Greatest and Least Values 194Problems to Be Solved Without Assistance (920-951) 199Answers and Hints 2