Life of Fred: Geometry (Expanded Edition)

Life of Fred Geometry Expanded – All you would want to know and more

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Thirteen regular chapters and six bonus honors chapters.

  • 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.


(All the answers are given in the book itself. No need to buy answer keys, teachers’ editions, or anything else.)

Click here to download a sample.