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Full Description
Classical Euclidean geometry, with all its triangles, circles, and inscribed angles, remains an excellent playground for high-school mathematics students, even if it looks outdated from the professional mathematician's viewpoint.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 self-study (some with hints). Each chapter also provides concise reminders of basic notions used in the chapter, so the book is almost self-contained (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 high-school 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.
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
