Geometry Chapter 1 Flashcards

Always

• Intersecting lines are always coplanar, meaning they lie within the same plane.
• Three points are always coplanar, as any three points can be connected through a single plane.
• A plane containing two points of a line always contains the entire line extending through both points.
• Two parallel lines are always coplanar, as parallel lines exist in the same plane without intersecting.
• Opposite rays always form a line by extending in opposite directions from a shared endpoint.
• Two planes that do not intersect are always parallel, maintaining a constant distance apart.
• A line and a point are always coplanar because any point can define a plane with a line.
• Two points are always collinear, since a line can always be drawn between them.
• Opposite rays always share the same endpoint, which defines their origin.

Never

• Two planes never meet in exactly one point; they either intersect along a line or are parallel.
• Two lines never meet in more than one point; they can either intersect at a single point or be parallel.
• Skew lines are never coplanar, as they do not lie in the same plane and do not intersect.
• Parallel lines are never skew, as they exist within the same plane and do not meet.

Sometimes

• Four points are sometimes coplanar; they can be coplanar if they lie on the same plane, but it's not guaranteed.
• Two lines in the same plane are sometimes parallel; they may be parallel if they do not intersect, but can also intersect.
• Two lines that lie in parallel planes are sometimes parallel, depending on their orientation.

Skew Lines

• Skew lines are always noncoplanar; they do not lie within the same plane.