Question

сформулируйте аксиому параллельных прямых

Answer 1

через точку не лежащую на прямой можно провести только одну прямую параллельную данной

Answer 2

Axiom of Parallel Lines

The axiom of parallel lines is a fundamental concept in geometry that deals with the relationship between parallel lines. It states that if two lines are parallel to the same line, then they are parallel to each other. In other words, if two lines do not intersect a third line, then they are parallel to each other.

This axiom is often used as a starting point in geometric proofs and is essential in the development of Euclidean geometry. It provides a basis for understanding the properties and relationships of parallel lines and angles.

Example: Let's consider three lines, A, B, and C. If line A is parallel to line B, and line B is parallel to line C, then according to the axiom of parallel lines, line A is also parallel to line C.

This axiom is widely accepted and forms the foundation of many geometric principles and theorems. It allows us to make deductions and draw conclusions about the properties of parallel lines and the angles formed by them.

Please note that the sources provided do not contain specific information about the axiom of parallel lines. However, this concept is widely taught and accepted in geometry education and can be found in various geometry textbooks and educational resources.