Translated from Russian by Marie Brodsky with assistance from Gina Yatsenko, Ray Droujkov, and Artem Astapchuk.
Softcover ISBN:  9781470419219 
Product Code:  MCL/18 
List Price:  $35.00 
Individual Price:  $26.25 
eBook ISBN:  9781470430115 
EPUB ISBN:  9781470468415 
Product Code:  MCL/18.E 
List Price:  $30.00 
Individual Price:  $22.50 
Softcover ISBN:  9781470419219 
eBook: ISBN:  9781470430115 
Product Code:  MCL/18.B 
List Price:  $65.00 $50.00 
Translated from Russian by Marie Brodsky with assistance from Gina Yatsenko, Ray Droujkov, and Artem Astapchuk.
Softcover ISBN:  9781470419219 
Product Code:  MCL/18 
List Price:  $35.00 
Individual Price:  $26.25 
eBook ISBN:  9781470430115 
EPUB ISBN:  9781470468415 
Product Code:  MCL/18.E 
List Price:  $30.00 
Individual Price:  $22.50 
Softcover ISBN:  9781470419219 
eBook ISBN:  9781470430115 
Product Code:  MCL/18.B 
List Price:  $65.00 $50.00 

Book DetailsMSRI Mathematical Circles LibraryVolume: 18; 2016; 214 ppMSC: Primary 51
Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for highschool mathematics students, even if it looks outdated from the professional mathematician's viewpoint. It provides an excellent choice of elegant and natural problems that can be used in a course based on problem solving.
The book contains more than 750 (mostly) easy but nontrivial problems in all areas of plane geometry and solutions for most of them, as well as additional problems for selfstudy (some with hints). Each chapter also provides concise reminders of basic notions used in the chapter, so the book is almost selfcontained (although a good textbook and competent teacher are always recommended). More than 450 figures illustrate the problems and their solutions.
The book can be used by motivated highschool students, as well as their teachers and parents. After solving the problems in the book the student will have mastered the main notions and methods of plane geometry and, hopefully, will have had fun in the process.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
What a joy! Shen's “Geometry in Problems” is a gift to the school teaching world. Beautifully organized by content topic, Shen has collated a vast collection of fresh, innovative, and highly classroomrelevant questions, problems, and challenges sure to enliven the minds and clever thinking of all those studying Euclidean geometry for the first time.
This book is a spectacular resource for educators and students alike. Users will not only sharpen their mathematical understanding of specific topics but will also sharpen their problemsolving wits and come to truly own the mathematics explored. Also, Math Circle leaders can draw much inspiration for session ideas from the material presented in this book.
—James Tanton, MathematicianatLarge, Mathematical Association of America
We learn mathematics best by doing mathematics. The author of this book recognizes this principle. He invites the reader to participate in learning plane geometry through carefully chosen problems, with brief explanations leading to much activity. The problems in the book are sometimes deep and subtle: almost everyone can do some of them, and almost no one can do all. The reader comes away with a view of geometry refreshed by experience.
—Mark Saul, Director of Competitions, Mathematical Association of America
Titles in this series are copublished with the Mathematical Sciences Research Institute (MSRI).
ReadershipStudents, teachers, math circles organizers, parents, and others interested in teaching and learning basic plane geometry.

Table of Contents

Chapters

Measuring line segments

Measuring angles

The triangle inequality

Congruent figures

Triangle congruence tests

Isosceles triangles

Circle

Straightedge and compass constructions

Parallel lines

Right triangles

Parallelograms

Rectangle, rhombus, square

Graph paper

Equilateral triangles

Midsegment of a triangle

Intercept theorem

Trapezoid

Simple inequalities

Reflection symmetry

Central symmetry

Angles in a circle

Tangents

Two circles

Circumscribed circle and perpendicular bisectors

Inscribed circle (incircle). Bisectors

Inscribed and circumscribed quadrilaterals

Area

The Pythagorean Theorem

Similarity

Coordinates on a line

Coordinates on a plane

Common measure

Trigonometry

Afterword


Additional Material

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Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for highschool mathematics students, even if it looks outdated from the professional mathematician's viewpoint. It provides an excellent choice of elegant and natural problems that can be used in a course based on problem solving.
The book contains more than 750 (mostly) easy but nontrivial problems in all areas of plane geometry and solutions for most of them, as well as additional problems for selfstudy (some with hints). Each chapter also provides concise reminders of basic notions used in the chapter, so the book is almost selfcontained (although a good textbook and competent teacher are always recommended). More than 450 figures illustrate the problems and their solutions.
The book can be used by motivated highschool students, as well as their teachers and parents. After solving the problems in the book the student will have mastered the main notions and methods of plane geometry and, hopefully, will have had fun in the process.
In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.
What a joy! Shen's “Geometry in Problems” is a gift to the school teaching world. Beautifully organized by content topic, Shen has collated a vast collection of fresh, innovative, and highly classroomrelevant questions, problems, and challenges sure to enliven the minds and clever thinking of all those studying Euclidean geometry for the first time.
This book is a spectacular resource for educators and students alike. Users will not only sharpen their mathematical understanding of specific topics but will also sharpen their problemsolving wits and come to truly own the mathematics explored. Also, Math Circle leaders can draw much inspiration for session ideas from the material presented in this book.
—James Tanton, MathematicianatLarge, Mathematical Association of America
We learn mathematics best by doing mathematics. The author of this book recognizes this principle. He invites the reader to participate in learning plane geometry through carefully chosen problems, with brief explanations leading to much activity. The problems in the book are sometimes deep and subtle: almost everyone can do some of them, and almost no one can do all. The reader comes away with a view of geometry refreshed by experience.
—Mark Saul, Director of Competitions, Mathematical Association of America
Titles in this series are copublished with the Mathematical Sciences Research Institute (MSRI).
Students, teachers, math circles organizers, parents, and others interested in teaching and learning basic plane geometry.

Chapters

Measuring line segments

Measuring angles

The triangle inequality

Congruent figures

Triangle congruence tests

Isosceles triangles

Circle

Straightedge and compass constructions

Parallel lines

Right triangles

Parallelograms

Rectangle, rhombus, square

Graph paper

Equilateral triangles

Midsegment of a triangle

Intercept theorem

Trapezoid

Simple inequalities

Reflection symmetry

Central symmetry

Angles in a circle

Tangents

Two circles

Circumscribed circle and perpendicular bisectors

Inscribed circle (incircle). Bisectors

Inscribed and circumscribed quadrilaterals

Area

The Pythagorean Theorem

Similarity

Coordinates on a line

Coordinates on a plane

Common measure

Trigonometry

Afterword