DG is a given line segment with points D E F G on the segment in order from left to right as shown in the given image.
1. DF = EG (Given)
2. As, DF=DE+EF
and EG=EF+FG
Also, DF=EG (Given)
Substituting the values of DF and EG in the given equation,
DE+EF = EF+FG (Substitution property of equality)
Subtracting EF from both the sides ,
DE=FG (Subtraction property of equality).
The answered table is attached.