To determine the next step in constructing a parallel line to \(CD\), let's review the standard process for constructing parallel lines:
1. Start by drawing a line through point B that you want to make parallel to \(CD\), or identify point B and line \(CD\) if they are already given.
2. Use a compass to draw an arc that intersects line \(CD\) at two points, let's call these points E and F.
3. Without changing the width of the compass, place the compass point on B and draw a similar arc that intersects the initial line (constructed through B) at two points.
4. Adjust the compass width to match the distance between points E and F (the intersections of the arc with \(CD\)).
5. Using this compass width, mark this distance on the new arc drawn through point B.
Let's analyze the answer choices:
A. Set the compass width to be where the arc intersects lines EC and EB.
- This doesn't quite make sense in this context as it incorrectly suggests identifying intersections with lines EC and EB.
B. Using the same compass width that created the first arc, repeat the arc centered at point B.
- This is part of the standard method, suggesting to draw a similar arc with the same radius from point B.
C. Set the compass width to the distance between point E and where the arc crosses line AB.
- This is a step that would typically come after repeating the arc centered at point B.
D. Using the same compass width that created the first arc, repeat the arc centered at point C.
- Usually, after drawing the first arc, the next step involves the intersection at point B, not C.
Given these options, **B: Using the same compass width that created the first arc, repeat the arc centered at point B** is the logical next step in constructing a parallel line to \(CD\). This would ensure a consistent radius to be used later to mark out equal distances, crucial for drawing parallel lines properly.
Based on the construction shown, what is the next step in the process of constructing parallel line CD?
A. Set the compass width to be where the arc intersects lines EC and EB.
B. Using the same compass width that created the first arc, repeat the arc centered at point B.
C. Set the compass width to the distance between point E and where the arc crosses line AB.
D. Using the same compass width that created the first arc, repeat the arc centered at point C.
1 answer