Jaymie wants to construct congruent angles with a

Jaymie and Annie both want to create congruent angles and segments using a compass and straightedge. Let's explore the similarities and differences in their construction steps.

Similarities:
1. Both Jaymie and Annie will be using a compass and straightedge for their constructions.
2. They will both begin with a given angle or segment that serves as a reference.

Differences:
1. Jaymie's Construction Steps for Congruent Angles:
  a. Place the compass point at the vertex of the given angle.
  b. Without changing the compass width, draw an arc that intersects both arms of the angle.
  c. Keeping the compass width unchanged, move the compass to the vertex of another angle.
  d. Draw an arc from the second vertex to intersect the previously drawn arc.
  e. Without changing the compass width, draw an arc from the second vertex to intersect the other arm of the second angle.
  f. The intersection of the arcs will determine the congruent angle.

2. Annie's Construction Steps for Congruent Segments:
  a. Place the compass point at one endpoint of the given segment.
  b. Open the compass to any convenient width.
  c. Without changing the compass width, draw an arc that intersects the segment.
  d. Keep the compass width unchanged and place the compass point at the other endpoint of the segment.
  e. Draw another arc that intersects the previous arc.
  f. Without changing the compass width, place the compass point at the intersection of the arcs.
  g. Draw an arc that intersects both arcs.
  h. The intersection of the arcs will determine the congruent segment.

In summary, Jaymie constructs congruent angles by using intersecting arcs, while Annie constructs congruent segments by using intersecting arcs as well. Both methods involve using a compass and straightedge, but the specific steps and geometric elements involved differ.