Question

Select the correct answer. based on the construction shown, what is the next step in the process of constructing parallel line ? a straight line ab has a mid-point e such that ceb forms an acute angle a. set the compass width to be where the arc intersects lines and . b. using the same compass width that created the first arc, repeat the arc centered at point c. c. using the same compass width that created the first arc, repeat the arc centered at point b. d. set the compass width to the distance between point e and where the arc crosses line .

Answer 1

The correct next step in the process of constructing parallel lines is option (b). Using the same compass width that created the first arc, repeat the arc centered at point c.

Step-by-step explanation:

In constructing parallel lines through the given process, the critical step is to maintain the consistent compass width used to create the initial arc. This ensures geometric accuracy and parallelism. The midpoint e of line ab is pivotal in this construction. Option (b) correctly directs us to repeat the arc centered at point c with the same compass width.

To elaborate, the acute angle angle CEB formed at the midpoint e is crucial for maintaining parallelism. By setting the compass width to the intersection of lines ce and eb (where the arc crosses lines e and eb, option (b) ensures the parallelism criterion. This step aligns with the geometric principle that corresponding angles formed by a transversal cutting parallel lines are congruent.

Additionally, options (a) and (c) do not maintain the consistent compass width, introducing potential errors in the construction. Option (d) is not aligned with the geometric constraints of the given construction process. Therefore, option (b) stands as the correct and precise next step in constructing parallel lines based on the provided information.