What Are the Steps in Proving Lines Are Parallel?

Parallel lines are lines along the same plane that never intersect, even though they are of infinite length. If you are working on a construction project, it is important to make sure that segments that are supposed to be parallel actually are. To prove that two lines are parallel, you need a square or a protractor and a straight edge.

  1. Start a perpendicular ray

    Choose one of the lines you believe to be parallel. Mark a point on the line where you could easily begin a perpendicular line. Use your square or protractor to find a ninety degree angle taken at that point. Using your straight-edge tool, draw a ray starting at the point you marked and pointing toward the other parallel line.

  2. Extend the ray to the second line

    Use your straight-edge tool to extend the perpendicular ray. Continue until it intersects with the second line. Check at different points along this perpendicular ray to make sure it stayed as straight as possible, especially if you are measuring over a great distance.

  3. Check the angle of the new intersection

    Use your square or protractor to check the angle created at the new intersection. If it is also 90 degrees, the lines are approximately parallel. In parallel lines, the corresponding angles created by an intersecting line are equal.