Coplanar lines are either parallel or intersecting.
Always True (my answer)
Sometimes True
Never True
Any three distinct collinear points are coplanar
True
False (my answer)
Two lines that do not intersect no matter how far you are going to extend them are parallel
Always True (my answer)
Sometimes True
Never True
Non-intersecting lines are noncoplanar.
Always True
Sometimes True (my answer)
Never True
#1. ok
#2. Any three distinct collinear points are coplanar
How can this not be true? Every line lies in some plane, so any set of collinear points must lie in a plane.
3 points determine a plane, unless they are collinear, but they still must lie in the same plane(s). Many planes contain a line, and so must also cintain the three points in that line.
#3. false - skew lines do not intersect, and they are not parallel
they are not coplanar.
#4. ok - I'm surprised that you got this, but not #3.
oh, yeah shoot. Thanks
For num 2, I read it as "Any three distinct coplanar points are collinear"
My bad
For num 3 though, I answered "sometimes true", neither false nor true
Anyway, thank you
To determine the truth value of each statement, we need to understand the concepts involved.
1. Coplanar lines are either parallel or intersecting:
This statement is always true. Two lines that lie in the same plane can either be parallel and never intersect or they can intersect at a single point.
2. Any three distinct collinear points are coplanar:
This statement is always true. Collinear points lie on the same line, and since lines are considered to be coplanar, any three collinear points will also be coplanar.
3. Two lines that do not intersect no matter how far you extend them are parallel:
This statement is always true. When two lines do not intersect no matter how far you extend them, they are considered parallel.
4. Non-intersecting lines are noncoplanar:
This statement is sometimes true. If two lines do not intersect and are not in the same plane, then they are noncoplanar. However, if the lines are in the same plane but simply don't intersect, then they are still considered coplanar.
So, the correct answers are:
1. Always True
2. Always True
3. Always True
4. Sometimes True