# Euclidean Geometry

## Topic outline

- Welcome
### Welcome

Geometry as a discipline is concerned with the relationships between shapes and spaces.

It was a very important subject that was studied and taught at centres of higher learning in ancient Greece. The Greek philosopher Plato established his Academy in Athens in 387 BCE. Some historical sources state that there was a notice inscribed above the entrance to the Academy reading: "Let no-one ignorant of geometry enter here".

Why are we studying "Euclidean" geometry? Because Euclid was a Greek mathematician (around 300 BCE) who pulled together our knowledge of geometry into a logical whole. He taught us an approach to mathematical thought that we still apply today.

Starting with basic definitions and axioms that we hold to be true, we carry these ideas to their logical conclusions by stating and demonstrating or proving the truth of theorems. Euclidean Geometry is a system of accurate definitions, clearly stated assumptions, and proof based on logical deduction.

### Euclidean Geometry

We will look back at knowledge gained in earlier grades, but add to this as follows:

1. The necessary and sufficient conditions for polygons to be similar;

2. Proportionality in triangles;

3. Equiangular triangles are similar;

4. Triangles with sides in proportion are similar;

5. The theorem of Pythagoras.Quizzes: 2Lessons: 7URL: 1Forum: 1File: 1

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