Question

this diagram was created by starting with points a and b and using only a straightedge and compass to construct the rest. all steps of the construction are visible. describe precisely the straightedge and compass moves required to construct the line cd in this diagram.

Explanation:

Step1: Open compass to distance AB

Place the compass - point on A and adjust the compass width to reach B.

Step2: Draw arcs

With the compass - point on A, draw an arc above and below the line segment that will approximately be where CD is. Then, without changing the compass width, place the compass - point on B and draw similar arcs above and below the line segment. These arcs will intersect at two points.

Step3: Use straightedge

Place the straightedge on the two intersection points of the arcs and draw the line CD.

Answer:

1. Open the compass to the length of AB.
2. With the compass centered at A, draw two arcs (one above and one below the expected line CD).
3. With the same compass - setting (width equal to AB), center the compass at B and draw two more arcs (above and below) to intersect the previous arcs.
4. Use a straightedge to draw a line through the intersection points of the arcs, which is the line CD.