True/false-if 2 paralel planes are cut by a 3rd plane, then the lines of the intersection can't intersect?

True. since they're parallelTrue/false-if 2 paralel planes are cut by a 3rd plane, then the lines of the intersection can't intersect?
True because if they where to intersect this point would be on both of the parallel planes which by definition have no point in commonTrue/false-if 2 paralel planes are cut by a 3rd plane, then the lines of the intersection can't intersect?
One of the lines is on one plane. The other line is on the other plane. There's no point that's even on both PLANES at once, so in particular there's no point that's on both lines at once.





That's why it's true.
Draw a picture.


The planes are parallel, so what are the ';lines of intersection'; going to look like?


Imagine a bookshelf, and there are two shelves you're trying to fit a book in between. But the book is too big, height-wise, to fit in there. That's the third plane... but imagine if you could fit that book through there, so that the ends were sticking past each shelf. Lines would be formed as the book intersected the two shelves. Those lines would be parallel, because the shelves are parallel.


So they're parallel - will they ever intersect?
True. The two lines of intersection are parallel.