Question

question 1 of 5
select the correct answer.
use a compass and straight edge to create a line parallel to line ab through a point e that is not on line ab. first, draw a line from point e that crosses line ab, and label the intersection point c.
which step comes next?

• set the compass point on a and draw an arc of any size across line ab.
• set the compass width to the width of the arc that crosses line ab.
• place the point of the compass on c and draw an arc that crosses both lines.
• move the compass point to the upper arc and mark off an arc, creating point d.

Explanation:

To construct a line parallel to \( AB \) through point \( E \), after drawing the transversal \( EC \) (intersecting \( AB \) at \( C \)), the next step in the compass - and - straightedge construction (using the method of corresponding angles or equal arcs) is to set the compass width to the arc that crosses \( AB \). This is because we first create an arc on \( AB \) with the compass centered at \( A \) (or \( C \) in the transversal context), and then we need to transfer that arc length to the transversal at \( E \). The first option about drawing an arc from \( A \) is the initial arc on \( AB \), and after that, we set the compass width to that arc's length (the arc crossing \( AB \)) to use it for the parallel line construction. So the step that comes next is "Set the compass width to the width of the arc that crosses line \( AB \)".

Answer:

Set the compass width to the width of the arc that crosses line \( AB \) (the third option in the list of options provided)