Question

prove: ( de = fg )
1 ( df = eg ) given
2
validate please select a rule

Explanation:

Step1: Express \(DF\) and \(EG\) in terms of segments

From the line - segment \(DF = DE+EF\) (by the segment - addition postulate, which states that if \(E\) lies between \(D\) and \(F\), then \(DF=DE + EF\)) and \(EG=FG + EF\) (by the segment - addition postulate, since \(F\) lies between \(E\) and \(G\)).

Step2: Substitute into the given equation

Since \(DF = EG\) (given), we substitute the expressions from Step 1: \(DE+EF=FG + EF\).

Step3: Use the subtraction property of equality

Subtract \(EF\) from both sides of the equation \(DE+EF=FG + EF\). By the subtraction property of equality (\(a + c=b + c\Rightarrow a=b\)), we get \(DE=FG\).

Answer:

\(DE = FG\) is proved as shown above.