Prove and use slope criteria for parallel and perpendicular lines.
Use slope to show two segments are parallel
Problem
For noncollinear segments \(AB\) and \(CD\) with \(A(0,1)\), \(B(4,3)\), \(C(-2,1)\), \(D(2,3)\), calculate \(\text{both}~\text{slopes}\), compare them, and determine whether the segments are parallel.
Treat each segment as a direction vector and compute signed rise over signed run with one subtraction order per segment. Equal slopes show equal direction only after the supporting lines are known to be distinct; otherwise the segments could simply lie on the same line.
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