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定理:三个平面两两相交于三条交线,这三条交线相交于一点或互相平行。(证明略)在有些解有关三线平行或三线共点的习题时,例1 空间四边形ABCD各边上取点E、F、G、H四点,且EFHG是平面图形。(1)若EF∥GH则EF∥BD;(2)若EF与GH相交,则交点在BD上。证明:∵三平面ABD、CBD、EFHG两两相交,其交线为BD、EF、GH。(1)∵EF∥GH,∴EF∥BD。
Theorem: The three planes intersect at the intersection of three lines, and the three lines intersect at one point or parallel to each other. (Proof is abbreviated) When there are some solutions to the problem of three-line parallel or three-point common problem, the points of E, F, G, and H on the sides of ABCD of example 1 are taken as four points, and EFHG is a plane figure. (1) If EF∥GH then EF∥BD; (2) If EF and GH intersect, the intersection point is on BD. Proof: The three planes ABD, CBD, and EFHG intersect each other, and their intersections are BD, EF, and GH. (1) ∵EF∥GH, ∴EF∥BD.