Final answer:
To copy ∠ABC correctly, draw an arc from B that intersects both rays, use the same compass width to draw an arc from D, transfer the distance between intersection points on the first arc to the second arc, then draw a ray from D through the new point to create the angle.
Step-by-step explanation:
To correct the construction for copying ∠ABC with point D as the vertex, we first need to establish that the initial steps mentioned in the description are creating a copy of ∠ABC at point D. Given the instructions, it seems that there may be a misunderstanding. The correct procedure for copying an angle should involve the following:
- Draw an arc across both rays of the angle with a compass centered at the vertex B, where the arc intersects the rays, label these points J and K.
- Without changing the compass width, draw a similar arc from point D, this new arc intersects the ray from D at point L.
- Measure the distance between points J and K with the compass, and without changing the compass width, transfer this distance starting from point L to mark point M on the arc centered at D.
- Draw a ray from point D through point M; this will be the copy of ∠ABC with D as the vertex.
It is important that the radius of the arcs and the distance between points J and K are kept consistent when transferring these to the new angle at point D to ensure that the angles are congruent. Additionally, make sure the direction in which the angle is being replicated is clear, as this will determine on which side of the ray from point D point M should lie.