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### Life of Fred: Geometry

by Stanley F. Schmidt, Ph.D.
\$39.00
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
• 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.
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
• 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