The rule used to prove show or build parallel lines depends very much on the information available and the circumstances of the event.
You can prove that two lines are parallel if you can show that they have the same slope. No other rule is necessary but, of course, you need enough information to form an equation or find m(the gradient or slope) . Convert given (linear) equations into the standard form of `y=mx+c` which will reveal m. Or use `(y_(2) - y_(1))/(x_(2) - x_(1)) = m` depending on available information. If m is the same, you can draw two parallel lines.
If there are angles that equal each other, such as corresponding angles or alternate angles, this information alone is also enough to create parallel lines. In other words, if a line that transverses two (seemingly) parallel lines, has angles that equal each other (congruent) in the format for corresponding or alternate angles, then they are parallel. The existence of co-interior angles equalling 180 degrees also proves lines are parallel.
Ans: When a TRANSVERSAL cuts two lines and equal angles or co-interior angles are formed, any ONE piece of information in terms of this rule is sufficient.
Two lines that have the same SLOPE are parallel.