Final answer:
The question appears to ask about proving line segments to be parallel, but lacks sufficient detail for a conclusive answer. Techniques involve comparing angles or slopes, but more context is needed for a specific solution.
Step-by-step explanation:
The question seems to be asking how to prove that two line segments are parallel using given geometrical or algebraic information, such as equal angle measures (m<1=m) or consistent slope values. However, the necessary details to provide a conclusive answer are incomplete. To determine if line segments are parallel, one might look for corresponding angles being equal, alternate interior angles being equal, or slopes of the lines being equal if the question were in a coordinate plane context.
When determining the slope of a line in a coordinate plane, one can use two points on the line, preferably points that are far apart, to minimize the impact of any errors in measurement. This is done using the formula (y2 - y1) / (x2 - x1), which gives the rate of change along the straight line.