Question

a) if ef = 16, then fg and eg = ? b) if rs = 42, then fr and fs = ?

Explanation:

Step1: Identify equal - length segments

From the figure, we can see that \(EF = FG\) and \(FR=FS\) because of the congruence marks.

Step2: Solve part A

Given \(EF = 16\), since \(EF = FG\), then \(FG=16\). And \(EG=EF + FG\), so \(EG=16 + 16=32\).

Step3: Solve part B

Given \(RS = 42\), and \(RS=FR + FS\), also \(FR = FS\). Then \(FR=FS=\frac{42}{2}=21\).

Answer:

A. \(FG = 16\), \(EG = 32\)
B. \(FR = 21\), \(FS = 21\)