Life of Fred: Geometry, Expanded Edition
Hardcover; ISBN: 9781937032210
Geometry is the third book in the Life of Fred High School Mathematics Series, and is designed for students in 11th grade who have already finished the preceding Beginning Algebra, Expanded Edition and Advanced Algebra, Expanded Editionbooks.
Thirteen and a half chapters are included; half-chapters provide "honors-level" content that covers topics such as flawless modern geometry and symbolic logic. Each lesson ends with a "Your Turn to Play" segment with a small number of thought-provoking questions. Chapters conclude with six problem sets, each of which is named after a city. The book concludes with an ART (All Reorganized Together) section that provides a convenient summarization for test review. Unlike other Life of Fred books, only half of the answers are contained in this textbook; the other half are provided in the sold-separately "Life of Fred Geometry City Answer Key.
Geometry covers: Points and lines, Definition of when one point is between two other points, Definition of a triangle, Midpoint, Proof of a theorem in paragraph form, Tangent and secant lines, Area and volume formulas, Undefined terms, Hypothesis and conclusion, Contrapositives, Postulates, Euclid's The Elements, Rays, Acute, obtuse, and right angles, Congruent angles, Linear pairs, Vertical angles, Supplementary angles, Perpendicular lines, SSS, SAS, ASA, Isosceles triangle theorem, Pons Asinorum, Parallel lines, Skew lines, Indirect proofs, Attempts to prove the parallel postulate, Exterior angles, Two proofs of the exterior angle theorem, Hypotenuse-leg theorem, Medians, Quadrilaterals: parallelogram, rhombus, trapezoid, kite, rectangle, square, Honor's Problem of the century: If two angle bisectors are congruent when drawn to the opposite sides, then the triangle is isosceles, Definition of a polygon, Proofs of all the area formulas given only the area of a square (This is hard. Most books start with the area of a triangle as given.) Proofs of the Pythagorean theorem, Geometries with only three points, Similar triangles, Five manipulations of proportions, Angle bisector theorem, Symbolic logic, Truth tables, Circles, Inscribed angle theorem, Definition of a limit of a function, Inductive and deductive reasoning, Golden rectangles, 46 Ruler-and-compass constructions, Non-euclidean geometries, Solid geometry, Euler's theorem, Geometry in high dimensions, Stereochemistry and homochirality, Complete chart up to the 14th dimension, Proofs using analytic geometry, Proof that a right angle is congruent to an obtuse angle using euclidean geometry, Flawless (modern) geoemtry which was invented about a hundred years ago.
Life of Fred is a unique, complete (not supplemental), math program that uses a highly engaging narrative to teach math without fear and with enjoyment. Students follow the life of Fred Gauss (a math professor who grows up to the age of six), who has many humorous, unlikely, and zany adventures over the course of the curriculum. Math becomes relevant and important because the need for math occurs in Fred's life (and he sees math everywhere). Witty and truly entertaining, these books will engage students in a way unlike any other math program - --while also instilling a solid understanding of the principles of mathematics without an abundance of repetitive drills. This series is perfect for inquisitive students who struggle with the relevance of math, or anyone looking for a creative approach to mathematic thinking!
542 pages, indexed; hardcover, non-consumable textbook with Smyth-sewn binding. Students write their answers on separate paper. Half of the answers are also included in the text and written directly to the student.