Question

the steps for copying $overline{ab}$ using a compass and straightedge are given. which sequence has the steps in the correct order?
1 place the point of the compass at $a$ and adjust the compass so that the pencil is at $b$.
2 draw a point at the intersection of the line and the arc. label the point $m$
3 $overline{ab} \cong overline{lm}$
4 draw a line and point $l$ on the line.
5 without adjusting the compass, place its point at $l$ and draw an arc that intersects the line that contains point $l$

\\(\bigcirc\\) a) 4, 5, 1, 2, 3
\\(\bigcirc\\) b) 4, 1, 5, 2, 3
\\(\bigcirc\\) c) 3, 1, 4, 2, 5
\\(\bigcirc\\) d) 1, 5, 2, 4, 3

Explanation:

To copy segment \( \overline{AB} \) to \( \overline{LM} \) using a compass and straightedge, the correct sequence of steps is as follows:

1. Step 4: First, draw a line and mark point \( L \) on it (this is the line where the copied segment will lie).
2. Step 1: Place the compass point at \( A \) and adjust it to reach \( B \) (to set the length of \( \overline{AB} \)).
3. Step 5: Without adjusting the compass, place its point at \( L \) and draw an arc intersecting the line (to transfer the length \( AB \) to the new line).
4. Step 2: Draw a point \( M \) at the intersection of the arc and the line (this becomes the endpoint of the copied segment).
5. Step 3: Conclude that \( \overline{AB} \cong \overline{LM} \) (verify the copy is congruent).

This matches the sequence in option B: \( 4, 1, 5, 2, 3 \).

Answer:

B. 4, 1, 5, 2, 3