Question

given: ( cf = eg ) ( cd = ef ) prove: ( df = fg ) 7 ( df = fg )

Explanation:

Step1: Use segment addition postulate

We know that \(CF = CD + DF\) (by segment addition postulate) and \(EG=EF + FG\) (by segment addition postulate).

Step2: Substitute given equalities

Since \(CF = EG\) (given) and \(CD = EF\) (given), we substitute into the equations from Step 1: \(CD + DF=EF + FG\).

Step3: Use subtraction property of equality

Subtract \(CD\) (which is equal to \(EF\)) from both sides of the equation \(CD + DF=EF + FG\). So \(DF=FG\) (by subtraction property of equality, if \(a + c=b + c\) and \(a = b\), then \(c\) is equal on both sides after subtraction)

Answer:

\(DF = FG\) (by subtraction property of equality)