Question

given a horizontal line segment ab and a point c, place the steps for copying \\(\overline{ab}\\) to create \\(\overline{cd}\\) in the proper order.

place the compass point at point c and draw an arc.
set the compass width to cb.
draw \\(\overline{cd}\\).
make a point d anywhere on the arc.
place the compass point at point b and draw an arc.
set the compass width to ab.

Explanation:

Step1: Set compass width to AB

To copy segment \( \overline{AB} \), first set the compass width equal to the length of \( \overline{AB} \). So, "Set the compass width to \( AB \)."

Step2: Place compass at C, draw arc

Now, place the compass point at point \( C \) (the starting point of the new segment) and draw an arc. This arc will be used to locate point \( D \). So, "Place the compass point at point \( C \) and draw an arc."

Step3: Make point D on arc

Next, make a point \( D \) anywhere on the arc drawn from point \( C \). This point \( D \) will be the endpoint of the new segment \( \overline{CD} \). So, "Make a point \( D \) anywhere on the arc."

Step4: Draw \( \overline{CD} \)

Finally, draw the segment \( \overline{CD} \) connecting points \( C \) and \( D \). So, "Draw \( \overline{CD} \)."

Wait, actually, the correct order for copying a segment \( \overline{AB} \) to \( \overline{CD} \) (with \( C \) as one endpoint) is:

1. Set the compass width to \( AB \) (measure the length of \( \overline{AB} \)).
2. Place the compass point at \( C \) and draw an arc (to create a locus of points at distance \( AB \) from \( C \)).
3. Make a point \( D \) on the arc (this will be the other endpoint, so \( CD = AB \)).
4. Draw \( \overline{CD} \).

But let's re - evaluate the given steps. The steps provided are:

• Set the compass width to \( AB \).
• Place the compass point at point \( C \) and draw an arc.
• Make a point \( D \) anywhere on the arc.
• Draw \( \overline{CD} \).

The other steps like "Set the compass width to \( CB \)" and "Place the compass point at point \( B \) and draw an arc" are incorrect for copying \( \overline{AB} \) to \( \overline{CD} \).

So the correct order of the valid steps (from the given list) is:

1. Set the compass width to \( AB \).
2. Place the compass point at point \( C \) and draw an arc.
3. Make a point \( D \) anywhere on the arc.
4. Draw \( \overline{CD} \).

Answer:

1. Set the compass width to \( AB \).
2. Place the compass point at point \( C \) and draw an arc.
3. Make a point \( D \) anywhere on the arc.
4. Draw \( \overline{CD} \).