Through the point of intersection of straight lines AB and AC, a straight line is drawn and not lying with them in the same plane. Prove that straight lines a and BC do not intersect
Lines AB and BC intersect at point A, therefore these lines lie in the same plane.
The straight line BC intercepts the straight lines AB and BC, which means that the straight line BC lies in this plane.
Line “a” intersects the plane at one point A, and therefore does not lie at this point. Point A does not lie on the straight line BC, and therefore the straight line BC cannot have common points with the straight line “a”, which means that they are intersecting and do not intersect, which is what was required to be proved.
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