Introduction

Euclidean geometry is the study of plane and solid figures based on axioms and theorems employed by the ancient Greek mathematician Euclid. It forms the foundation of most modern geometry taught in schools.

Euclid’s Five Postulates

1. A straight line can be drawn between any two points.
2. A finite straight line can be extended continuously in a straight line.
3. Given any straight line segment, a circle can be drawn having the segment as radius and one endpoint as center.
4. All right angles are congruent.
5. If a line falling on two lines makes interior angles on the same side less than two right angles, the two lines, if extended indefinitely, meet on that side.

Fundamental Concepts

• Point: an exact location with no dimensions.
• Line: a collection of points extending infinitely in both directions.
• Plane: a flat surface extending infinitely.
• Angle: the figure formed by two rays sharing a common endpoint.
• Triangle: a polygon with three edges and three vertices.

Key Theorems

Some classic results include:

• Pythagorean theorem
• Sum of interior angles in a triangle is 180°
• Congruent triangles (SSS, SAS, ASA, AAS)
• Similarity criteria (AA, SSS, SAS)

Applications

Euclidean geometry is used in:

• Architecture and engineering
• Computer graphics
• Navigation and mapping
• Robotics path planning

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