The figure shows a construction completed by hand.
The construction has a given segment AB. A ray has been created from point C. There is an arc on ray C that was created with a compass that is the same distance between points A and B. The arc creates point D on ray C.
Does the construction demonstrate how to copy a segment correctly by hand? Explain why or why not by describing how it was constructed.
No, the construction does not demonstrate how to copy a segment correctly by hand.
To copy a segment correctly by hand, we would need to use a compass to create congruent segments. However, in this construction, the distance between points A and B is not being copied correctly.
The construction only creates an arc with a radius equal to the distance between points A and B. This arc intersects with ray C at point D, but this does not ensure that the segment CD is congruent to segment AB.
A correct construction to copy a segment AB by hand would involve the following steps:
1. Place the compass point on point A and draw an arc that intersects segment AB at two points.
2. Without changing the compass width, place the compass point on one of the intersection points and draw an arc that intersects the previous arc.
3. Draw a straight line connecting the second intersection point with point A. This line will be congruent to segment AB.