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Life of Fred: Geometry

by Stanley F. Schmidt, Ph.D.
The third book in the Life of Fred High School Series.

  • Acute, obtuse, and right angles
  • Alternate interior angles and corresponding angles
  • Congruent angles
  • Degrees, minutes, and seconds
  • Euclid's The Elements
  • Exterior angles
  • Inscribed angle theorem
  • Linear pairs
  • Rays
  • Supplementary angles
  • Two proofs of the exterior angle theorem
  • Vertical angles
  • Area and volume formulas
  • Heron's Formula
  • Parallelograms
  • Perimeter
  • Polygons
  • Pythagorean Theorem
  • Rectangles, Rhombuses, and Squares
  • Trapezoids
  • Triangle inequality
  • Triangles
  • Center, radius, chord, diameter, secant, tangent
  • Concentric circles
  • Central Angles
  • Circumference
  • Arcs
  • Inscribed angles
  • Proof by Cases
  • Sectors
  • Compass and straightedge
  • Rules of the Game
  • Rusty compass constructions
  • Golden Rectangles and golden ratio
  • Trisecting an angle and squaring a circle
  • Incenter and circumcenter of a triangle
  • Collapsible compass constructions
  • 46 popular constructions
  • Analytic geometry
  • Cartesian/rectangular/orthogonal coordinate system
  • Axes, origins, and quadrants
  • Slope
  • Distance formula
  • Midpoint formula
  • Proofs using analytic geometry
  • Proof that every triangle is isosceles
  • Proof that an obtuse angle is congruent to a right angle
  • 19-year-old Robert L Moore's modern geometry
  • Geometry in Four Dimensions
  • Geometry in high dimensions
  • Complete chart up to the 14th dimension
  • Stereochemistry and homochirality
  • Five manipulations of proportions
  • Tesseracts and hyper tesseracts
  • Definition of a polygon
  • Golden rectangles
  • Proof of a theorem in paragraph form
  • Hypothesis and conclusion
  • Indirect proofs
  • Hunch, hypothesis, theory, and law
  • 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
  • Definition of a limit of a function
  • Inductive and deductive reasoning
  • Proofs using geometry
  • Attempts to prove the Parallel Postulate
  • Nicolai Ivanovich Lobachevsky's geometry
  • Consistent Mathematical theories
  • Georg Friedrich Bernhard Riemann's geometry
  • Geometries with only three points
  • Attempts to prove the parallel postulate
  • Collinear points
  • Concurrent lines
  • Coplanar lines
  • Coordinates of a point
  • Definition of when one point is between two other points
  • Exterior Angles
  • Indirect Lines
  • Line segments
  • Midpoint
  • Parallel lines
  • Perpendicular Lines
  • Perpendicular Bisectors
  • Postulates and theorems
  • Skew lines
  • Distance from a point to a Line
  • Tangent and secant lines
  • Theorems, propositions, lemmas, and corollaries
  • Undefined terms
  • Honors Problem of the century:
    If two angle bisectors are congruent
    when drawn to the opposite sides,
    then the triangle is isosceles
  • Intercepted segment
  • Kite
  • Midsegment of a triangle
  • Parallelogram
  • Rectangle
  • Rhombus
  • Square
  • Trapezoid
  • Euler's theorem
  • A line perpendicular to a plane
  • Distance from a point to a plane
  • Parallel and perpendicular planes
  • Polyhedrons: hexahedron (cube), tetrahedron, octahedron, icosahedron, dodecahderon
  • Volume Formulas: cylinders, prisms,
    cones, pyramids, spheres
  • Cavalieri's Principle
  • Lateral Surface Area
  • Contrapositives
  • If...then...statements
  • Truth tables
  • Acute and Obtuse Triangles
  • Adjacent, opposite, hypotenuse
  • Altitudes
  • Angle bisector theorem
  • Definition of a triangle
  • Drawing auxiliary lines
  • Equilateral and equiangular triangles
  • Hypotenuse-leg theorem
  • Isosceles triangle theorem
  • Medians
  • Pons Asinorum
  • Proof that a right angle is congruent to an obtuse angle using euclidean geometry
  • Proportions
  • Right Triangles
  • Scalene Triangles
  • Similar triangles
  • SSS, SAS, ASA postulates
Sku #: 684

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by Stanley F. Schmidt, Ph.D.