## Gusev, Litvinenko, Mordkovich – Solving Problems in Geometry

In this post, we will see the book  Solving Problems in Geometry by
V. 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 of
problems in geometry found at school. The book contains about 1000
problems 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 by Mir in 1988.

PDF | Bookmarked | Cover

Preface 5
Chapter 1. PLANE GEOMETRY 10

Sec. 1. Methods of Solving Geometrical Problems 10
II. Circles 12
III. Areas of Plane Figures 13

Sec. 2. Triangles and Quadrilaterals 22
Problems to Be Solved Without Assistance 28
I. Right Triangles (1-12) 28
II. Isosceles Triangles (13-31) 29
III, Arbitrary Triangles (32-59) 30
IV, Parallelograms (60-73) 31
V. Trapezoids (74-92) 32
VI, Miscellaneous Problems (93-110) 33

Sec. 3. Circles 34
Problems to Be Solved Without Assistance 40
I. Circles (111-129) 40
II. Inscribed and Circumscribed Triangles (130-157) 41
III. A Circle and a Triangle Arranged Arbitrarily (158-175) 43
IV, A Circle and a Quadrilateral (176-191) 44
V, Miscellaneous Problems (192-219) 45

Sec. 4, Areas of Plane Figures 47
Problems to Be Solved Without Assistance 57
I. Area of Triangles (220-247) 57
II. Area of Quadrilaterals (248-271) 59
III. Area of Polygons (272-279) 60
IV. Area of Combined Figures (280-295) 61
V, Miscellaneous Problems (296-321) 62

Sec. 5. Geometrical Transformations 64
Problems to Be Solved Without Assistance 68
I. Symmetry with Respect to a Point (322-337) 68
II. Symmetry About a Straight Line (338-362) 69
III. Rotation (363-377) 70
IV. Translation (378-390) 71
V. Homothetic Transformation (391-397) 72

Sec. 6. Vectors 73
I. Affine Problems 75
II. Metric Problems 81
Problems to Be Solved Without Assistance 83
I. Addition and Subtraction of Vectors, Multiplication of a Vector
by a Number (398-436) 83
II. Scalar Product of Vectors (437-457) 86
III. Miscellaneous Problems (458-534) 87

Sec. 7. Greatest and Least Values 92
Problems to Be Solved Without Assistance (535-562) 101

Chapter 2. SOLID GEOMETRY 103

Sec. 8. Constructing the Representation of a Given Figure 1 H3

Sec. 9. Geometrical Constructions in Space 114
I. Simplest Constructions in Space 114
II. Loci of Points 115
III. Applications of Certain Loci of Points and Straight Lines 117
IV. Constructions on Representations 118
Problems to Be Solved Without Assistance 126
I, Simplest Constructions in Space (563-569) 126
II. Loci of Points (570-583) 126
III. Applications of Certain Loci of Points and Lines (584-592) 127
IV. Constructions on Representations 127
(1) Constructing Plane Figures in Space (593-597) 127
(2) Section of a Polyhedron by a Plane Parallel to Two Straight
Lines (598-607) 127
(3) Constructing a Perpendicular to a Straight Line and a
Perpendicular to a Plane (608-617) 128
(4) Section of a Polyhedron by a Plane Passing Through a Given
Point Perpendicular to a Given Line (618-621) 129
(5) Constructing a Locus of Points Equidistant from Given Points
(622-630) 129

Sec. 10. Skew Lines. Angle Between a Straight Line and a Plane 130
Problems to Be Solved Without Assistance (631-689) 130

Sec. 11. Dihedral and Polyhedral Angles 143
Problems to Be Solved Without Assistance (690-723) 140

Sec. 12. Sections of Polyhedrons 148
Problems to Be Solved Without Assistance (724-762) 159

Sec. 13. Surfaces 162
Problems to Be Solved Without Assistance (763-799) 170

Sec. 14. Volumes 172
Problems to Be Solved Without Assistance (800-852) 17a

Sec. 15. Combinations of Polyhedrons and Circular Solids 183
Problems to Be Solved Without Assistance (853-919) 1S9

Sec. 16. Greatest and Least Values 194
Problems to Be Solved Without Assistance (920-951) 199

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### 4 Responses to Gusev, Litvinenko, Mordkovich – Solving Problems in Geometry

1. m95 says:

Thanks for all for this nice post

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2. Siddharth says: