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

1. we don't get to see the figure, so we don't know. If there is no figure, then it would be "sometimes true", since they have a common point J.

2. Two planes, if they meet, would meet along a line. Sometime they don't meet at all (parallel). So it is never true.

Well, let's see if we can bring some humor to these mathematical concepts!

- Is it always true that ray LJ and ray TJ are opposite rays? Well, unless LJ and TJ are secretly long-lost twin rays who were separated at birth and magically reunited, we can safely say that they are opposite rays. So, the answer is...always true! Opposites do attract, after all!

- Now, let's move on to the intersection of two planes being a point. Imagine you have two planes on a blind date, hoping to find a connection. But alas, when they meet, they realize they are just too plane...er, plain for each other! So, it's sometimes true, but not always. Sometimes planes intersect in a whole line or even infinitely many points. It's not always a magical "point" of connection!

Remember, humor is subjective, but I hope I managed to bring a smile to your face while tackling these math questions!

- Ray LJ and Ray TJ are opposite rays: It is always true that Ray LJ and Ray TJ are opposite rays. Opposite rays are two collinear rays that share the same endpoint and extend in opposite directions.


- The intersection of two planes is a point: It sometimes true that the intersection of two planes is a point. If the two planes are different and not parallel, they will intersect at a single point. However, if the two planes are parallel or coincide, they will intersect in a line or infinitely many points, respectively.

To determine whether a statement is always, sometimes, or never true, we need to analyze the statement and consider all possible scenarios.

1. Ray LJ and ray TJ are opposite rays:
To determine if this statement is always, sometimes, or never true, we need to understand what opposite rays are. Opposite rays are two rays that extend in opposite directions from the same endpoint, forming a straight line.

To determine if LJ and TJ are always opposite rays, we need to consider all possible scenarios. If LJ and TJ do not share the same endpoint, they cannot be opposite rays since they need to emanate from the same point. Therefore, the statement is sometimes true, depending on the configuration of the rays.

2. The intersection of two planes is a point:
To determine the validity of this statement, we need to understand the properties of planes. A plane is a two-dimensional flat surface that extends infinitely in all directions. The intersection of planes can vary depending on their orientation.

In general, the intersection of two planes can be a line, a point, or even empty if the planes are parallel and do not intersect. However, if the two planes are not parallel, the intersection will always be a line.

Therefore, the statement "The intersection of two planes is a point" is sometimes false, since the intersection can also be a line or empty depending on the scenario.

In summary:
1. The statement "Ray LJ and ray TJ are opposite rays" is sometimes true, depending on whether LJ and TJ share the same endpoint.
2. The statement "The intersection of two planes is a point" is sometimes false, as the intersection can also be a line or empty depending on the orientation of the planes.