Identify one of the steps necessary to construct a parallel line to a given line through a point not on the line.(1 point)

Question

Responses which is the true correct answer and why

With the pointed tip of your compass on a point on the given line, draw an arc that extends both above and below the given line.
With the pointed tip of your compass on a point on the given line, draw an arc that extends both above and below the given line.

After drawing a given line and a point not on the line, fold your paper so that the fold goes through the point not on the line.
After drawing a given line and a point not on the line, fold your paper so that the fold goes through the point not on the line.

Place the edge of a ruler on the given line and slide the ruler up or down until it is aligned with the point, then draw a line through the point.
Place the edge of a ruler on the given line and slide the ruler up or down until it is aligned with the point, then draw a line through the point.

With the pointed tip of your compass on a point on the given line, draw an arc that intersects the given line and the line drawn from the point on the given line to the point not on the given line.

Answer 1

The correct step to construct a parallel line to a given line through a point not on the line is:

"With the pointed tip of your compass on a point on the given line, draw an arc that intersects the given line and the line drawn from the point on the given line to the point not on the given line."

Why this is the correct answer:

This step involves using a compass to create arcs that facilitate the transfer of angles, which is crucial for constructing parallel lines. The method works by finding points of intersection that maintain the same distance (angle) as the original line. When you draw an arc with the compass placed on a point on the given line, you can then use the intersection points to ensure that the line through the point not on the original line is parallel. This method is in line with Euclidean geometry principles, where parallel lines maintain equal distances and angles relative to one another.

The other options either do not involve geometric properties necessary to ensure parallelism or are less conventional approaches to achieving the task.