Lesson's in Geometry
Geometry is a subject in Mathematics that has been around for ages. One of the earliest people to write down the principles of Geometry was the Greek philosopher Euclid. In the mid 1800's, John Playfair translated Euclid's works into English [1].

Lesson 1 - EUCLID's Definitions - Illustrated

The works of Euclid begin with some basic definitions. Using the Geometer's Sketch pad, I have illustrated these definitions.

Lesson 2 - EUCLID's Postulates and Axioms

In addition to the definitions, Euclid spelled out what Playfair called postulates and axioms. These provide a framework for what has been come to be known as Euclidean geometry.

The works of Euclid are separated in several different "books." Within each book are propositions about geometrical objects. A proposition can be a statement of some truth that can be proven. This is called a theorem. A proposition can also be a problem. This is a way to construct or draw a geometric figure. Both can be proven to be true. The proof uses the definitions, postulates, axioms, and propositions already proven. The following lessons are based on these two types of propositions.

Lesson 3 - Proposition I - Problem. Constructing an equilateral triangle

Proof of construction for an equilateral triangle

Lesson 4 - Proposition II - Problem. Constructing equal straight lines

Proof of construction of equal straight lines

Lesson 5 - Proposition III - Problem. Constructing a part of a line equal to a shorter line

Proof of construction of part of a line equal to a shorter line

Lesson 6 - Proposition IV - Theorem - Equality of triangles

Lesson 7 - Proposition V - Theorem - Equality of angles

Lesson 8 - Proposition VI - Theorem - Equality of sides

Lesson 9 - Proposition VII - Theorem - Uniqueness of triangles

Lesson10 - Proposition VIII - Theorem - Another case of equal angles

Lesson 11

Propositions IX through XII are construction problems. The reader is encouraged to construct the proof of these on his or her own.

Proposition IX - Bisecting an angle

Proposition X - Bisecting a line

Proposition XI - Drawing a right angle

Proposition XII - Drawing a perpendicular to a line

There are many more constructions and theorems in geometry. I hope you have profitted from the ones here and will explore others.

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