Question

is the following statement true or false?
the intersection of a plane and a line segment can be a line segment.
true false

Explanation:

Step1: Analyze the intersection concept

A plane and a line segment can intersect in different ways. If the line segment lies on the plane, then their intersection is the line segment itself. Also, even if the line segment is not fully on the plane, but a part of it (a sub - segment) lies on the plane, the intersection would be that sub - segment (a line segment). For example, consider a line segment with endpoints \(A\) and \(B\), and a plane that contains a part of the line segment from \(A\) to a point \(C\) (where \(C\) is between \(A\) and \(B\)). Then the intersection of the plane and the line segment \(AB\) is the line segment \(AC\).

Step2: Conclude the truth value

From the above analysis, we can see that the intersection of a plane and a line segment can be a line segment. So the statement is true.

Answer:

true