If two lines are both parallel to a third line, then…
they are parallel to each other. (All 3 lines are parallel.)
If two planes are both parallel to a third plane, then…
they are parallel to each other. (All 3 planes are parallel.)
If two lines are both perpendicular to a third line, then…
No conclusion... They could be parallel or they could be skew or they could intersect.
If two coplanar lines are both perpendicular to a third line, then…
they are parallel.
If two planes are both perpendicular to a third plane, then…
No conclusion... They could be parallel or perpendicular or they could just intersect.
If two lines are both perpendicular to the same plane, then…
they are parallel.
If two planes are both perpendicular to the same line, then…
they are parallel.
If a line is perpendicular to one of two parallel planes, then…
it is perpendicular to the other.
If a plane is perpendicular to one of two parallel lines, then…
it is perpendicular to the other.
**If a plane intersects two parallel planes, then…
the lines of intersection are parallel.
Be ready to explain the following statements:
If 2 lines are parallel to the same plane, no conclusion can be made.
If 2 planes are parallel to the same line, no conclusion can be made.