Proving Lines are Parallel

So I am thinking about Open Middle problems, transformations and parallel lines.  As an 8th grader, is there more than 3 ways to “prove” two line segments are parallel?


Method 1: Slope

Parallel Lines1

Slope of line a = 2/5, slope of line b = 2/5.  Since the slopes are equal, they are parallel.


Method 2: Line of Reflection

Parallel Lines2

Find a line l so that when you fold on that line, line a and line b match up perfectly.


Method 3: Translation

Parallel Lines3

Find a Translation where every point from line a will map to its corresponding point on line b-> (X+4, Y-2).


(Method 2 and 3 may not be as formally worded here, just trying to anticipate possible student answers)

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