Thales' theorem in space

Thales’ theorem, known from the plane, has a spatial version in which the parallel lines are replaced by parallel planes.

Theorem — Thales' theorem in space

A pencil of parallel planes cut by two transversal lines determines proportional segments on the two lines: $\frac{AB}{BC} = \frac{A'B'}{B'C'}.$

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Topics: Synthetic geometry of space
Concepts: Thales’ theorem
Skills: Synthetic geometry
People: Thales