Final answer:
The false statement about trisecting segments with a compass and straightedge is D: A segment cannot be trisected using a compass and a straightedge. This statement is incorrect because while an angle cannot be trisected with these tools alone, a segment certainly can be.
Step-by-step explanation:
The question 'Which statement about trisecting segments with a compass and straightedge is false?' requires an understanding of basic geometric constructions. When we look at the options provided:
- A. Trisecting a segment divides it into three equal segments. This is true.
- B. One step in trisecting a segment is to construct parallel segments. While constructing parallel lines may be part of some construction processes, it is not specifically necessary for trisecting a segment, but this statement is technically not false.
- C. To trisect a segment, start by drawing a ray from the endpoint of the segment. This is also a true step in the process of constructing a trisection of a segment.
- D. A segment cannot be trisected using a compass and a straightedge. This statement is false. In accordance with the classic problem of the trisection of an angle, a segment can indeed be trisected using a compass and straightedge; however, trisecting an angle (which is a different task) is what cannot be done with these tools alone.
The correct answer to the question is D. A segment can be trisected using a compass and a straightedge.