Question

Drag an expression or statement to each box to complete the proof.

It is given that E is the midpoint of DF. So, DE
the
DE+EF=DF by the
by substitution. Simplifying gives 2DE=DF
by the definition of midpoint. Therefore, DE= EF by
segment congruence postulate segment addition postulate DF
EF
and so DE+DE=
DF DE

Answer 1

The question involves completing a geometric proof to show that segment DE is equal to segment EF using the segment addition postulate, definition of midpoint, and segment congruence postulate.

Step-by-step explanation:

The student's question pertains to a geometric proof involving the midpoint of a segment. The question involves completing a geometric proof to show that segment DE is equal to segment EF using the segment addition postulate, definition of midpoint, and segment congruence postulate.

The proof relies on various geometry postulates and definitions to establish the relationship between different segments of a line. To complete the proof that E is the midpoint of DF:

1. DE = EF by the definition of midpoint.
2. DE + EF = DF by the segment addition postulate.
3. By substitution, we use the fact that DE = EF to write DE + DE = DF.
4. Simplifying the expression gives 2DE = DF.
5. Therefore, DE = EF by the segment congruence postulate.