MathDB

6

Part of 1987 Czech and Slovak Olympiad III A

Problems(1)

Parallel lines in space

Source: Czech and Slovak Olympiad 1987, National Round, Problem 6

4/10/2020
Let AA′,BB′,CC′AA',BB',CC' be parallel lines not lying in the same plane. Denote UU the intersection of the planes A′BC,AB′C,ABC′A'BC,AB'C,ABC' and VV the intersection of the planes AB′C′,A′BC′,A′B′CAB'C',A'BC',A'B'C. Show that the line UVUV is parallel with AA′AA'.
Parallel Linesgeometry3D geometrynational olympiad