Life of Fred Geometry Expanded

Description

One day in Fred’s life in which he . . .
• Falls in Love!
• Teaches you how to write an opera!
• Buys Hecks Kitchen!
• Does all of geometry up to the 14th dimension!

Geometry is one course that is different from all the rest. In the other courses, the emphasis is on calculating, manipulating and computing answers. In contrast, in geometry there are proofs to be created. It is much more like solving puzzles than grinding out numerical answers. For example, if you start out with a triangle that has two sides of equal length, you are asked to show that it has two angles that have the same size.

You will need at least one year of high school algebra. (Life of Fred: Beginning Algebra). In this geometry book for example, on p. 26 we will go from y + y = z to y = ½ z. It is preferable, however, that you have completed the two years of high school algebra. (Life of Fred: Beginning Algebra and Life of Fred: Advanced Algebra Expanded Edition). Most schools stick geometry between the two years of algebra – beginning algebra, geometry, advanced algebra – but there are a couple of reasons why this is not the best approach.

First, when you stick geometry between the two algebra courses, you will have a whole year to forget beginning algebra. Taking advanced algebra right after beginning algebra keeps the algebra fresh.

Second, the heart of geometry is learning how to do proofs. This requires an “older mind” than the mechanical stuff in the algebra courses. A person’s brain develops in stages. Most three-year-olds don’t enjoy quiz shows on television.

In this course you will learn about…
Non-Euclidean 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
Points and Lines
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
Quadrilaterals
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
Solid Geometry
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
Symbolic Logic
Contrapositives
If…then…statements
Truth tables
Triangles
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
Angles
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
Area and volume formulas
Heron’s Formula
Parallelograms
Perimeter
Polygons
Pythagorean Theorem
Rectangles, Rhombuses, and Squares
Trapezoids
Triangle inequality
Triangles
Circles
Center, radius, chord, diameter, secant, tangent
Concentric circles
Central Angles
Circumference
Arcs
Inscribed angles
Proof by Cases
Sectors
Constructions
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
Coordinate Geometry
Analytic geometry
Cartesian/rectangular/orthogonal coordinate system
Axes, origins, and quadrants
slope
distance formula
midpoint formula
proofs using analytic geometry
Flawless (Modern) 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 Dimensions
Geometry in Four Dimensions
Geometry in high dimensions
Complete chart up to the 14th dimension
Stereochemistry and homochirality
Five manipulations of proportions
tesseracts and hypertesseracts
Polygons
Definition of a polygon
Golden rectangles
Proofs
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
Unlike all other math programs, this one also has:
• The only verse of Fred’s famous song, “Another Day, Another Ray”
• The difference between iambic, trochaic, anapestic and dactyllic in poetry
• How easy it is to confuse asinorum which is in the genitive plural in Latin with asinus which is in the nominative singular.
• A good use for Prof. Eldwood’s Introduction to the Poetry of Armenia while on the deck of a pirate ship

All answers are included in the textbook.





More Ways to Learn Geometry

Homeschool Geometry Curriculum

6th - 9th | Online class

MathHelp.com offers a comprehensive homeschool Geometry curriculum. Our stand-alone curriculum has everything your child needs, including efficient, professional instruction throughout every lesson.

2nd Grade Math Worksheets: Geometry

2nd | Worksheet/Printable

Our grade 2 geometry worksheets focus on deepening students understanding of the properties two dimensional shapes, including the concepts of congruency, symmetry, area and perimeter. We also...

Lumos Functions and Geometry Skill Builder, Grade 8

8th | Book

This book is designed to help eighth grade students practice and master Functions and Geometry. Taking the time to study and practice each standard individually can help students more adequately...

Preschool Geometry Worksheets

Pre-K | Printable

Preschool shapes worksheets are the perfect way to teach your child about all the different kinds of shapes. Try our preschool shapes printables with your kid.

Free
Offers paid add-ons

Geometry Content Inventory

9th - High School | Online resource

Virtual Nerd’s patent-pending tutorial system provides in-context information, hints, and links to supporting tutorials, synchronized with videos, each 3 to 7 minutes long. In this non-linear...

Geometry and spatial reasoning

Pre-K - 9th | Online resource

Practice geometry and spatial reasoning skills on IXL, have fun, and win awards!

$10 monthly

Geometry Lesson Series

6th - High School | Online resource

Students use the geometry lessons in this series to explore and learn essential geometric postulates, theorems, and formulas through video and text. Students will confirm their learning with...

Geometry Course

High School | Online resource

Geometry covers points, lines, planes, angles, parallel lines, triangles, similarity, trigonometry, quadrilaterals, transformations, circles and area. The material is text and video lectures, but...

Crafty Cut

5th - High School | iPhone/iPad

Crafty Cut is a block slicing game that offers three creative game modes dealing with 2D and 3D geometry. This app can be downloaded for free, but the complete version requires purchase. There is...

Mathventure for 3rd Grade: Focus on Geometry

3rd | iPhone/iPad, Mac OS

Read a free sample or buy Mathventure for 3rd Grade: Focus on Geometry by S. Lemay & J.C. Hamel. You can read this book with iBooks on your iPhone, iPad, iPod touch, or Mac.

Mathventure for 4th Grade: Focus on Geometry

4th | iPhone/iPad, Mac OS

Designed by experienced authors, the Mathventure collection facilitates implementation of the Common Core Math Standards. The interactive books in this collection put students in meaningful...

Geometry: Intro to Proofs

High School | Product, Windows

This highly intensive course, designed by Stanford mathematicians, teaches students geometry through the lens of formal logic. Not only will students learn geometric properties, but they will also...

Shiny Party

Pre-K - 1st | iPhone/iPad

Learn shapes and colors Shiny Party is a fun learning app that promotes essential basic geometry skills. Kids will learn to identify shapes and colors, explore ways in which shapes can be joined...

Prentice Hall Mathematics Geometry

9th - High School | Product


Traditional geometry concepts are highlighted through this text. Your child will learn to visualize and see relationships between two figures, relate mathematical functions with figures, measure...

Geometry

Kindergarten - 2nd | Online class

Learn how different shapes have different numbers of corners, different side lengths, and so on. Use these properties to help you recognize shapes.

Transformations, congruence, and similarity

9th - College | Online class

Learn about geometric transformations and how they’re used to understand the meaning of “similar” and “congruent”.

Geometry

4th - High School | Online class

Roughly 2400 years ago, Euclid of Alexandria wrote Elements which served as the world’s geometry textbook until recently. Studied by Abraham Lincoln in order to sharpen his mind and truly...

Basic geometry

3rd - 7th | Online class

Let’s draw points, lines, line segments, and rays. We’ll also think about perpendicular and parallel lines and identify these in two-dimensional figures. Common Core Standard: 4.G.A.1

Measurement and geometry

2nd - 4th | Online class

In 2nd grade, you learned to measure lengths. Now we can measure the length around the edge of an object (perimeter) and how much “space” something takes up on a flat surface (area).

Analytic Geometry

6th - 9th | Online class

In analytic geometry, also known as coordinate geometry, we think about geometric objects on the coordinate plane. For example, we can see that opposite sides of a parallelogram are parallel by by...

Geometry

9th - High School | Book, Online class

Geometry introduces students to mathematics as a deductive science. It shows how a few simple assumptions about points, lines, etc., can lead to a substantial body of geometric theorems and the...

$150
Offers paid add-ons

Geometry

3rd - 6th | Online class

Let’s draw points, lines, line segments, and rays. We’ll also think about perpendicular and parallel lines and identify these in two-dimensional figures. Common Core Standard: 4.G.A.1

Geometry (online)

9th - High School | Online class

This online course gives students a comprehensive introduction to Euclidean geometry and the principles of logical reasoning. After an introduction to the GradPoint interface and the basic tools...

$150
Offers paid add-ons

Special properties and parts of triangles

9th - College | Online class

In this tutorial, we study lines that are perpendicular to the sides of a triangle and divide them in two (perpendicular bisectors). As we’ll prove, they intersect at a unique point called the...

Tutor in a Book's Geometry

6th - 9th | Book

Need help with Geometry? Designed to replicate the services of a skilled private tutor, the new and improved Tutor in a Book’s Geometry is at your service! TIB’s Geometry is an extremely thorough,...

Geometry DVD Instruction

9th - High School | DVD

This course is designed to help students improve their problem solving and deductive reasoning through the study the geometric points, lines, and shapes. It covers the practical subjects related to...

Geometry

4th - 6th | Online class

We’re going to stick our toes into the proverbial waters of geometry! For those of you that are visual learners you’ll love this topic. We’ll examine all kinds of lines and shapes in the 1st, 2nd,...

Math Curriculum Geometry

High School | Online resource

Geometry Introduction to Geometry Unit Preview, Definitions – Geometry, Measuring Angles – Geometry, Line and Angle Relationships, Triangles, Definitions of Figures Construction Unit Preview,...

$360 yearly

Geometry

5th - 7th | Online class

Learn how to find the area, volume, and surface area of all sorts of geometric shapes. Also work with shapes on the coordinate plane.

Curriki Geometry

9th - High School | Online resource

This collection includes resources that are used throughout the six projects of Curriki Geometry. Curriki is grateful for the tremendous support of our sponsor, AT&T Foundation. Our TeamCurriki...


See all resources to Learn Geometry