Question

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

A)In space, there are at least four points that are not in the same plane.

B)If two planes intersect, then their intersection is a line.
C)Every plane contains at least two points that lie on the same line.
D)Given any two points A and B, there is exactly one line AB that passes through them.

Answer 1

it might be D.Given any two points A and B, there is exactly one line AB that passes through them. hope that help...

Answer 2

Answer with Explanation

Axioms are Intuitive, Instinctional .They can't be proved . They are universally true.

Option B is true, that is if two planes intersect, then their intersection is a line.

Option C, is also true, that if a line lies on a plane it will At least pass through two points on the plane.

Option D,if there are two points,only a unique line passes through them.Because to determine a line we need two different unique points.

So, Option 1,appears incorrect,which states that ,In space, there are at least four points that are not in the same plane.