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

*Update 12 Oct 2018: Added links to a new scan*

The Internet Archive Link

Table of Contents

Preface 5

**Chapter 1. PLANE GEOMETRY 10**

**Sec. 1. Methods of Solving Geometrical Problems 10**

I. Triangles and Quadrilaterals 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

Answers and Hints 202

Thanks for all for this nice post

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