Description
Book SynopsisTrade ReviewWhat 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
Table of Contents
- 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
