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## Solving Problems In Geometry

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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 Mir Publishers in 1988.

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 2

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## V. Litvinenko - Solving Problems in Geometry MIR

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## Solving Problems In Algebra and Trigonometry – Litvinenko, Mordkovich

In this post, we will see the book  Solving Problems In Algebra and Trigonometry – V. Litvinenko, A. Mordkovich. In an earlier post, we had seen the companion volume to this book Solving Problems in Geometry . The companion volume also has been updated with a fresh scan and new links have been added.

This study aid is intended for students of physical and mathemati­cal faculties of pedagogical institutes. The book contains about 2000 examples, problems, and exercises of which 1700 problems are for solving independently. Along with rather simple problems, there are also problems whose solution requires serious and sometimes inventive work. In the course of preparing the manuscript for print we tried to distribute the space among the basic types of “school” problems in algebra and trigonom­etry. Solving these problems will help the student to acquire pro­fessional skill necessary for a teacher who must know how to solve mathematical problems of the high-school level. This book is not only a collection of problems, it is rather a study aid for practical work, as can be seen in the structure of the text­ book. Each section contains necessary theoretical material and an ample number of worked examples (the total number of which amounts to about 300), which are very useful for the student pri­ marily from the methodological point of view.

The book was translated from the Russian by Leonid Levant and was first published by Mir in 1987.

PDF | Bookmarked | Cover

The Internet Archive Link

PART 1. ALGEBRA 7

Chapter 1. IDENTICAL TRANSFORMATIONS 7

Sec. 1. Factorization of Polynomials 7 Sec. 2. Identical Transformations of Rational Functions 11 Sec. 3. Identical Transformations of Irrational Functions 20 Sec. 4. Identical Transformations of Exponential and Logarith­mic Functions 29 Sec. 5. Proving Inequalities 33 Sec. 6. Comparing Numerical Expressions 41

Chapter 2. SOLVING EQUATIONS AND INEQUALITIES 45

PART II. TRIGONOMETRY 202

Chapter 3. IDENTICAL TRANSFORMATIONS 202

Sec. 21. Identical Transformations of Trigonometric Functions 202 Sec. 22. Transforming Functions Containing Inverse Trigonometric Functions 218 Sec. 23. Proving Inequalities 224

Chapter 4. SOLVING EQUATIONS AND INEQUALITIES 234

Sec. 24. Equations 234 Sec. 25. Systems of Equations 254 Sec. 26. Inequalities 265 Sec. 27. Parametric Equations and Inequalities 276

## About The Mitr

6 responses to solving problems in algebra and trigonometry – litvinenko, mordkovich.

You have some good books. Plus the intent is beautiful. I have some mir books, will share.

Do you have in stock this book Solving Problems in Algebra and Trigonometry my email is [email protected]

Can you please please please post Potapov Algebra and Analysis of Elementary Functions? This is the only one of Zeldovich’s references of which I cannot find a copy.

There’s a Spanish copy on libgen but no English copy unfortunately

There’s a Spanish copy on libgen but unfortunately not an English one

I am not sure what is the point you are making in the comment? There is an IA link to the English copy in the post.

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#### IMAGES

1. Solving problems in geometry / by V. Gusev, V. Litvinenko, A. Mordkovich

2. SOLVING PROBLEMS IN ALGEBRA AND TRIGONOMETRY. Translated from the Russian by Leonid Levant.: by

3. Especialistas em Livros de Exatas para IME ITA e Olimpíadas Solving Problems in Geometry

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1. Solving Problems In Geometry : V. Gusev; V. Litvinenko; A. Mordkovich

Solving Problems In Geometry ... V. Gusev, V. Litvinenko, A. Mordkovich. This book is intended for students at pedagogical (teacher training)

2. V. Gusev, V. Litvinenko

V. Gusev, V. Litvinenko - Solving Problems in Geometry.pdf - Free download as PDF File (.pdf) or view presentation slides online.

3. V. Litvinenko

V. Litvinenko - Solving Problems in Geometry MIR - Free download as PDF File (.pdf) or view presentation slides online.

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8. Solving Problems In Algebra and Trigonometry

This study aid is intended for students of physical and mathematical faculties of pedagogical institutes. The book contains about 2000 examples

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Feb 6, 2019 - Solving problems in geometry / by V. Gusev, V. Litvinenko, A. Mordkovich.