Question

consider the steps shown for bisecting an angle.
step description
1 place a compass at the vertex of the angle, and draw an arc from ray to ray of the angle.
2 label the points where the arc crosses the rays of the angles as points x and y.
3
4
5 label the point of intersection of the arcs as point z.
6 draw a ray from the vertex of the original angle to point z to create the angle bisector.
which steps best complete the table?
step 3: with point x as the center and the length of xy as the radius, draw an arc in the exterior of the angle. step 4: double the compass width, and draw an arc from point y in the interior of the angle.
step 3: with point x as the center and the length of xy as the radius, draw an arc in the interior of the angle. step 4: double the compass width, and draw an arc from point y in the interior of the angle.
step 3: with point x as the center and the length of xy as the radius, draw an arc in the exterior of the angle. step 4: keeping the compass width the same, draw an arc from point y in the interior of the angle.
step 3: with point x as the center and the length of xy as the radius, draw an arc in the interior of the angle. step 4: keeping the compass width the same, draw an arc from point y in the interior of the angle.

Explanation:

Step1: Analyze angle - bisecting principle

To bisect an angle using a compass and straight - edge, after getting points X and Y on the two rays of the angle, we need to create two intersecting arcs in the interior of the angle with equal radii.

Step2: Evaluate step 3

We should draw an arc in the interior of the angle with point X as the center and an appropriate radius. The radius is not necessarily the length of XY (but for the standard construction, we can use a radius that will help in getting the intersection point for the bisector). Here, we just need to create an arc in the interior of the angle with X as the center.

Step3: Evaluate step 4

To get the intersection point of the two arcs (point Z) which will be on the angle - bisector, we need to keep the compass width the same as that used for the arc with center X and draw an arc from point Y in the interior of the angle.

Answer:

Step 3: With point X as the center and an appropriate radius, draw an arc in the interior of the angle.
Step 4: Keeping the compass width the same, draw an arc from point Y in the interior of the angle.

(Note: In the given options, the most correct one is: Step 3: With point X as the center and the length of XY as the radius, draw an arc in the interior of the angle. Step 4: Keeping the compass width the same, draw an arc from point Y in the interior of the angle.)