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 solve it and tell me 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.

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.
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.

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.

Answer 1

The true correct answer is:

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.

Explanation:

This step is part of the classical geometric method for constructing a parallel line to a given line through a point not on that line, often using a compass and straightedge. Here's why this step is essential:

1. Establishing Reference Points: By drawing an arc that intersects the given line at two points (one above and one below), you create two reference points that define the orientation of the given line.

2. Transferring Angles: The next step typically involves using the distance between the two intersection points to set a compass width. This distance can then be used to replicate the angle or slope of the original line at the new point not on the line.

3. Geometric Construction: This method employs the principles of geometry, specifically the idea that parallel lines will maintain the same angle and distance apart. The arc helps ensure that when you construct the new line through the external point, it will be parallel to the original line because it maintains the same slope.

In summary, this step is critical because it lays the groundwork for accurate parallel line construction by establishing a relationship with the existing line through geometric reference points.