Suppose that the lines at and with intersect at some point O and form a triangle BCO.
The sum of the interior angles of a triangle is 180.
180 = OBC + OCB + BOC.
By condition, the straight line a is perpendicular to b and c, then the angle OBC = OCB = 90.
180 = 90 + 90 + BOC = 180 + BOC, then the angle BOC must be equal to 00, or a straight line in parallel to a straight line c, one hundred and it was required to prove.
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