Question

Which statement is NOT one of the axioms of Euclidean geometry?

A
Given any two distinct points, there is exactly one line that contains them.
B.
Every plane contains at least three points that do not lie on the same line.
C.
If two points lie in a plane, the line containing these points also lies in the plane.
D.
If two planes intersect, their intersection is a point.

Answer 1

Answer: The answer is (D).

Step-by-step explanation: We are given four statements and we to check which one is NOT an axiom of Euclidean geometry.

A. Given any two points, there is exactly one line that contains them. This is true and is one of the axioms of Euclidean geometry.

B. Every plane contains at least three points that do not lie on the same line. This is true and is one of the axioms of Euclidean geometry.

C. If two points lie in a plane, the line containing these points also lies in the plane. This is also true and is one of the axioms of Euclidean geometry.

D. If two planes intersect, their intersection is a point. This statement is false, because the intersection of two intersecting planes is always a line, not a point. Hence, it is NOT an axiom of Euclidean geometry.

Thus, the correct option is D.