Question

3
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.
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Explanation:

First, recall the core axioms (postulates) of Euclidean geometry:

1. Any two distinct points define exactly one line (matches option A).
2. A plane contains at least three non-collinear points (matches option B).
3. If two points lie in a plane, the line through them lies in the plane (matches option C).
4. When two planes intersect, their intersection is a line, not a point. This makes option D incorrect.

Answer:

D. If two planes intersect, their intersection is a point.