Given straight lines a, b, c. If a is perpendicular to c, b is perpendicular to c, then prove the parallelism of lines a and b.

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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