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 nonstandard approach. The solution of
moat 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.

  All credits to the original uploader.

  DJVU | 2.3 MB | Pages: 239 | OCR | Cover


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Table of Contents
Preface 5
Chapter 1. PLANE GEOMETRY 10

Sec. 1. Methods of Solving Geometrical Problems 10

Sec. 2. Triangles and Quadrilaterals 22

Sec. 3. Circles 34

Sec. 4, Areas of Plane Figures 47

Sec. 5. Geometrical Transformations 64 

Sec. 6. Vectors 73

Sec. 7. Greatest and Least Values 92

Chapter 2. SOLID GEOMETRY 103

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

Sec. 9. Geometrical Constructions in Space 114

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