Geometry in Problems

Alexander Shen, Institute of Problems of Information Transmission, Moscow, Russia, and LIRMM CNRS, Universite de Montpellier, France.

• Measuring line segmentsMeasuring anglesThe triangle inequalityCongruent figuresTriangle congruence testsIsosceles trianglesCircleStraightedge and compass constructionsParallel linesRight trianglesParallelogramsRectangle, rhombus, squareGraph paperEquilateral trianglesMidsegment of a triangleIntercept theoremTrapezoidSimple inequalitiesReflection symmetryCentral symmetryAngles in a circleTangentsTwo circlesCircumscribed circle and perpendicular bisectorsInscribed circle (incircle)BisectorsInscribed and circumscribed quadrilateralsAreaThe Pythagorean TheoremSimilarityCoordinates on a lineCoordinates on a planeCommon measureTrigonometryAfterword

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 classroom-relevant 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 problem-solving 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, Mathematician-at-Large, 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