# 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.

## Have you tried this resource?

Help someone out by sharing your thoughts!

### Have questions about K-12 education?

Ask our community of thousands of teachers, homeschoolers, and parents! Or see recently-asked questions.

## More Ways to Learn Geometry

\$50

### 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.

2
Free

### 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...

\$7

### 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...

\$67 yearly

### Geometry (3.0)

8th - High School | Book, DVD, Online class

The 3.0 is a per student online subscription that lasts for a full year (12 months). It works on ALL desktops and laptops, and it will even work on tablets and smartphones via the free Puffin...

Free

### 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

### 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...

\$10 monthly

### Geometry and spatial reasoning

Pre-K - 9th | Online resource

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

\$8

### 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...

\$15

### Mathventure for 3rd Grade: Focus on Geometry

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

\$6

### Mathventure for 4th Grade: Focus on Geometry

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...

\$124

### 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...

\$133

### 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...

Free

### 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.

Free

### 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”.

Free

### 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...

Free

### 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

Free

### 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).

Free

### 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...

Free

### 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

Free

### 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...

See all resources for Geometry

Links to supporting retailers are recognized and built automatically, so we can provide you with truly unbiased listings.
We receive a small share of sales from those links to help us keep this service free for all learners. Thanks for your support!