Answer:
- rays: DF and EF
- segments: ED, DF, FE
Explanation:
Given points D, E, F on a half-line with end point D, you want the names of two different rays and three different segments in the figure.
Ray
A ray is named by it endpoint and another point on the ray. Any of the named points could be the endpoint of a ray, but there is not another point to use for naming if F is the ray's endpoint.
The figure shows rays DE (congruent to ray DF) and ray EF.
Segment
A segment is named by naming its endpoints. Two of the three points shown can be chosen three different ways.
The figure shows segments DE, DF, and EF.
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Additional comment
Those segments could be named ED, FD, and FE. The question asks for different segments. Since DE and ED name the same segment, we can use only one of those names in answer to the question.