Question

Which of the following are among the five basic postulates of Euclidean geometry?

a) A line contains at least three points.
b) Through any two points, there exists exactly one line.
c) Two distinct lines intersect at more than one point.
d) There exists a line that does not lie in a plane.

Answer 1

Out of the options given, only option b) Through any two points, there exists exactly one line, is among the five basic postulates of Euclidean geometry.

Step-by-step explanation:

The five basic postulates of Euclidean geometry are:

1. A line contains at least two points.
2. Through any two points, there exists exactly one line.
3. A line can be extended indefinitely in both directions.
4. A circle with any point as its center and any radius can be drawn.
5. All right angles are congruent.

Out of the options given, only option b) Through any two points, there exists exactly one line, is among the five basic postulates of Euclidean geometry.