Question

Geometry 1. Which of the following may not be true? Select all that apply. A. If a point and a plane intersect, the intersection is a line. B. If two lines intersect, both lines are in one plane. C. If two lines intersect but do not coincide, the intersection is a point. D. If two planes intersect but do not coincide, the intersection is a line. E. If two points lie in a plane, then the line that contains the points is in that plane. F. There is exactly one line through any two points.​

Answer 1

Answer: B. If two lines intersect, both lines are in one plane.

F. There is exactly one line through any two points

Explanation:

The rest are true because I remember learning those in Geometry but B and F aren’t true because they just don’t make sense and aren’t true in general.

Answer 2

There are two statements that may not be true:

B. If two lines intersect, both lines are in one plane.

F. There is exactly one line through any two points.

Statement B is not true because if two lines intersect at an angle, they are not in the same plane. This is known as skew lines.

Statement F is not true in non-Euclidean geometries, such as spherical or hyperbolic geometry. In these geometries, there can be multiple lines that pass through two points. However, in Euclidean geometry (which is what is typically taught in high school), there is exactly one line that passes through any two points.

Explanation: