Determine if it is always sometimes never or always true
- ray LJ and ray TJ are opposite rays
-the intersection of two planes is a point
never
yes
To determine whether a statement is always, sometime, never, or always true, we can analyze the meaning of the statement and apply relevant mathematical concepts.
1. Ray LJ and ray TJ are opposite rays:
In geometry, opposite rays are two rays that share an endpoint and extend indefinitely in opposite directions. To determine if this statement is always, sometimes, or never true, we need to consider different possibilities. Let's assume that ray LJ and ray TJ share the endpoint J.
- If ray LJ extends indefinitely in the direction of JT, and ray TJ extends indefinitely in the direction of LJ, then they are opposite rays. In this case, the statement is always true.
- If ray LJ and ray TJ do not extend indefinitely in opposite directions, they are not opposite rays. For example, if they are parallel and do not intersect, the statement is never true.
- Alternatively, if they intersect at a point other than the common endpoint J, they are not opposite rays. In this case, the statement is never true.
Therefore, the statement "Ray LJ and ray TJ are opposite rays" is sometimes true since it depends on the specific configuration of the rays.
2. The intersection of two planes is a point:
In three-dimensional geometry, two planes can intersect in different ways, such as intersecting in a line or being parallel and not intersecting at all. To determine whether this statement is always, sometimes, never, or always true, we need to consider the different possibilities for the intersection of two planes.
- If two planes intersect at exactly one point, then the statement is sometimes true. This occurs when the two planes are not parallel and do not coincide.
- If two planes are parallel, they do not intersect, and the statement is never true.
- Additionally, if two planes coincide (meaning they are the same plane), then they intersect in infinitely many points, and the statement is always true.
Therefore, the statement "The intersection of two planes is a point" is sometimes true, depending on the relationship between the planes.