Given two intersecting lines a and b and a point A that does not lie on these lines. Lines m and n are drawn through point

Given two intersecting lines a and b and a point A that does not lie on these lines. Lines m and n are drawn through point A so that m⊥a, n⊥b. Prove that lines m and n do not coincide.

You need to start with the fact that lines a and b intersect, which means that they are NOT parallel. According to the axiom, we know that through a point that does not lie on a given straight line, one can draw a straight line parallel to it and only one. Following this statement, we say: if straight lines a and b are not parallel, then perpendicular straight lines emitted from the same point can NOT coincide, as they pass to different straight lines at different angles.