Question

If two planes, P1 and P2 are parallel, then (a) Any line in P1 is parallel to any line in P2 (b) AB =CD whenever points A and C are in P1 and points B and D are in P2 (c) Any line that intersects P1 in exactly one point will intersect P2 in exactly one point. (d) Any line that intersects P1 in more than one point must intersect P2 in more than one point.​

Answer 1

The assumptions mentioned about parallel planes are not entirely accurate. While any line in one parallel plane is indeed parallel to any line in another, the other propositions, including about points in separate planes being equidistant, or about lines intersecting the planes in certain ways, are incorrect.

Step-by-step explanation:

Let's examine each condition proposed about the two parallel planes, P1 and P2:

1. (a) Yes, any line in P1 is parallel to any line in P2 because the two planes are parallel.
2. (b) AB = CD doesn't necessarily hold true. The distance between two points in one plane does not have to correspond to the distance between two points in another plane, even if the planes are parallel.
3. (c) Wrong, a line that intersects P1 in exactly one point will not intersect P2 at all if the two planes are parallel.
4. (d) Also incorrect—a line that intersects P1 in more than one point would be contained entirely within that plane and thus would not intersect P2 at all, as the planes are parallel.

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