### 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
- 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.

$39.00