What are the basic axioms of Euclidean geometry?

Basic Axioms of Euclidean Geometry

Euclidean geometry is built on five fundamental rules called postulates (axioms), introduced by the ancient Greek mathematician Euclid:

• 1. A straight line can be drawn from any point to any other point.
• Example: You can draw a straight segment between points A and B.
• 2. A straight line segment can be extended indefinitely in a straight line.
• Example: Line segment AB can be extended as much as needed.
• 3. A circle can be drawn with any center and any radius.
• Example: With center O, and radius 2 units, you can draw a circle.
• 4. All right angles are congruent.
• Example: Any two right angles (each 90°) are equal in size.
• 5. (Parallel Postulate): If a line crossing two lines forms interior angles on the same side that sum to less than 180°, those lines will meet on that side if extended.
• Example: If transversal t intersects lines L and M such that the angles add up to less than 180°, L and M will intersect.

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Takeaway:

• Euclidean geometry is based on five intuitive postulates about points, lines, and circles.
• These axioms form the foundation for most geometry you study in school.