Question

question 1 - 6
alex needs to bisect \\( \angle a b c \\) using a compass and straightedge. he starts by completing the following steps.
step 1: place the compass on vertex \\( b \\) of the angle.
step 2: draw an arc that intersects both rays of the angle.
step 3: label these intersections as point \\( d \\) and point \\( e \\).
step 4: place the compass at point \\( d \\) and draw an arc in the interior of the angle.
which sequence of steps should alex take next in this construction?
\\( \bigcirc \\) adjust the compass width to be half the distance between point \\( b \\) and point \\( e \\), and then place the compass on point \\( e \\) and draw an arc in the interior of the angle that crosses the other arc.
\\( \bigcirc \\) adjust the compass width to be half the distance between point \\( b \\) and point \\( e \\), and then place the compass on point \\( e \\) and draw an arc on the exterior of the angle.
\\( \bigcirc \\) without adjusting the compass width, place the compass at point \\( e \\) and draw an arc on the exterior of the angle that is opposite the other arc.
\\( \bigcirc \\) without adjusting the compass width, place the compass at point \\( e \\) and draw an arc in the interior of the angle that crosses the other arc.

Explanation:

Step1: Analyze the angle - bisecting process

After labeling the intersections as \(D\) and \(E\) (Step 3), the next step in constructing an angle bisector is to use the same compass width (without adjusting it) to draw arcs.

Step2: Locate the compass position

We place the compass on one of the intersection points (either \(D\) or \(E\)) and draw an arc in the interior of the angle that crosses the other arc. Since we have already used the compass to draw the initial arcs from the vertex \(B\) (Step 1 - 2) and labeled the intersections \(D\) and \(E\) (Step 3), without adjusting the compass width (to maintain the same radius for congruent arcs), we place the compass at point \(E\) (or \(D\)) and draw an arc in the interior of the angle that crosses the other arc.

Answer:

Without adjusting the compass width, place the compass at point \(E\) and draw an arc in the interior of the angle that crosses the other arc.