If two straight lines cut one another, they are in one plane, and every triangle is in one plane.
若两条直线相交，则它们在同一平面内，且每个三角形也在同一平面内。
For let the two straight lines AB, CD cut one another at the point E; I say that AB, CD are in one plane, and every triangle is in one plane. For let points F, G be taken at random on EC, EB, let CB, FG be joined, and let FH, GK be drawn across; I say first that the triangle ECB is in one plane.
设两直线AB、CD相交于点E，需证AB、CD共面，且三角形ECB共面。
For, if part of the triangle ECB, either FHC or GBK, is in the plane of reference, and the rest in another, a part also of one of the straight lines EC, EB will be in the plane of reference, and a part in another.
在EC、EB上任取点F、G，连接CB、FG，并作FH、GK。先证三角形ECB在一平面内。
But, if the part FCBG of the triangle ECB be in the plane of reference, and the rest in another, a part also of both the straight lines EC, EB will be in the plane of reference and a part in another: which was proved absurd. [XI. 1] Therefore the triangle ECB is in one plane.
若三角形ECB的一部分（如FHC或GBK）在参考平面内，而其余部分在另一平面，则直线EC或EB的一部分在参考平面内，另一部分在另一平面，这与命题XI.1矛盾。
But, in whatever plane the triangle ECB is, in that plane also is each of the straight lines EC, EB, and, in whatever plane each of the straight lines EC, EB is, in that plane are AB, CD also.
因此三角形ECB在一平面内，而该平面也包含直线EC、EB，进而包含AB、CD（由XI.1）。