The figure shows a construction made using technology.
The construction shows angles CAB and IDE. There is a circle created from point A that intersects with ray AC, creating point F, and ray AB, creating point G. A circle congruent to circle A was created at point D. Circle D intersects with ray DE, creating point H. Another circle was created on point H that has a radius that is congruent to the distance between points F and G. Circle H intersects with circle D, creating point I. A ray was created through points D and I.
Does the construction demonstrate how to copy an angle correctly using technology? Explain why or why not by describing how it was constructed.
Yes, the construction demonstrates how to copy an angle correctly using technology.
To copy angle CAB, the construction first creates a circle with center at point A. This circle intersects with ray AC at point F and ray AB at point G. Then, a congruent circle is created at point D, which intersects with ray DE at point H. Next, a circle is created at point H with a radius that is congruent to the distance between points F and G. This circle intersects with circle D at point I. Finally, a ray is drawn through points D and I.
This construction accurately copies angle CAB because it ensures that angle IDE is congruent to angle CAB. The congruent circles created at points A and D ensure that the intercepted arcs created by ray AC and ray AB are congruent, resulting in equal angles at points F and G. When circle H intersects with circle D, point I is determined as the intersection point of the two arcs created by the congruent intercepted arcs at points F, G, and H. Therefore, angle IDE is congruent to angle CAB.
By following this construction, the angle CAB has been accurately copied using technology.