Question

given: e is the midpoint of df. prove: 2de = df drag an expression or statement to each box to complete the proof. it is given that e is the midpoint of df. so, de ≅ by the definition of midpoint. therefore, de = ef by the de + ef = df by the and so de + de = by substitution. simplifying gives 2de = df

Explanation:

Step1: Identify congruent segments

By the definition of midpoint, if \( E \) is the midpoint of \( DF \), then \( \overline{DE}\cong\overline{EF} \).

Step2: Use segment congruence postulate

The segment congruence postulate states that if two segments are congruent, then their lengths are equal. So, \( DE = EF \).

Step3: Apply segment addition postulate

The segment addition postulate states that if \( E \) lies on \( DF \), then \( DE+EF = DF \).

Step4: Substitute and simplify

Since \( DE = EF \), we substitute \( EF \) with \( DE \) in \( DE + EF=DF \). So, \( DE+DE = DF \), which simplifies to \( 2DE=DF \).

Answer:

1. \( \overline{EF} \)
2. segment congruence postulate
3. segment addition postulate
4. \( DF \)