When two parallel planes are sliced by a third, the two lines of intersection are always parallel, like the two faces of a sliced loaf of bread.
Module goal. Master systematically the tests and properties of parallel lines, line-and-plane, and plane-and-plane, and learn to convert freely among them.
eastmath.com · 28.6 Parallelism in Space: Tests and Properties · 28.6.4 Property of Two Parallel Planes