Question

which statement is not one of the axioms of euclidean geometry? select the correct answer. if two points lie in space, there is only one line that can pass through them. if two points lie on a plane, the line containing them also lies on the plane. if three points lie on the same line, there is only one plane that can pass through them. if two planes intersect, their intersection is a line.

Explanation:

• Recall Euclidean geometry axioms:
• Axiom: Through any two points, there is exactly one line (so the first option is an axiom).
• Axiom: If two points lie in a plane, the line containing them lies in the plane (so the third option is an axiom).
• Axiom: If two planes intersect, their intersection is a line (so the fourth option is an axiom).
• For three collinear points (on the same line), there are infinitely many planes that can pass through them (since a line lies on infinitely many planes), so the statement "If three points lie on the same line, there is only one plane that can pass through them" is not an axiom of Euclidean geometry.

Answer:

If three points lie on the same line, there is only one plane that can pass through them.