Final Answer:
Daniel's next step should be (a) Move the compass to point B and draw arcs intersecting the first ones.(Option a)
Step-by-step explanation:
To divide line segment AB into 6 equal parts using a compass, Daniel should follow a method known as compass and straightedge construction. The correct next step is to move the compass to point B and draw arcs intersecting the first ones. By doing this, Daniel creates 6 points of intersection on the line segment AB. These points will serve as the division points for the six equal partitions.
This construction technique relies on the principle that arcs drawn from two different points of intersection on a line will intersect at the same angle. The repetition of this process helps to accurately divide the line into the desired number of equal parts. Option (b) to draw a line connecting the points where the arcs intersect is not the immediate next step; rather, it is the final step to complete the division of the line segment.
In summary, the correct next step for Daniel is to move the compass to point B and draw arcs intersecting the first ones. This method ensures an accurate and geometrically sound partitioning of line segment AB into 6 equal parts using the compass and straightedge construction technique. (Option a)