The statement you provided appears to involve segments in a geometric context, likely in a triangle or similar figure. Here’s a way to express the reasons behind each equation:

1. **AE + EF = AF**: This can be justified by the Segment Addition Postulate, which states that if point E lies on segment AF, then the sum of the lengths of segments AE and EF is equal to the length of segment AF.

2. **CF + EF = CE**: Similarly, this can also be justified using the Segment Addition Postulate, indicating that if point E lies on segment CF, then the sum of the lengths of segments CF and EF equals the length of segment CE.

If you need further clarification or details on any of these points, feel free to ask! Here are some related questions to consider:

1. What specific geometric figure are AE, EF, AF, CF, and CE part of?
2. Can you provide a diagram to visualize these segments?
3. How do these segment relationships relate to any properties of triangles?
4. What is the significance of point E in this context?
5. Are there any other segment relationships that are relevant to this problem?

**Tip**: Always sketch a diagram when dealing with segment relationships to better visualize the problem and clarify your reasoning.

Explore the segment addition relationships AE + EF = AF and CF + EF = CE using the Segment Addition Postulate. This page breaks down the geometric concepts and provides insights for students in Grades 7-9.

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