Question

fghi ~ zwxy. find fi and gh.
fi =
gh =

Explanation:

Step1: Find the scale factor

Since \(FGHI\sim ZWXY\), the ratio of corresponding sides is the same. The ratio of \(HI\) to \(WX\) is \(\frac{HI}{WX}=\frac{4}{3}\). This is the scale factor.

Step2: Find \(FI\)

\(FI\) corresponds to \(XY\). Using the scale factor \(\frac{4}{3}\), we have \(FI=\frac{4}{3}\times XY\). Since \(XY = 2\), then \(FI=\frac{4}{3}\times2=\frac{8}{3}\).

Step3: Find \(GH\)

\(GH\) corresponds to \(ZY\). Using the scale factor \(\frac{4}{3}\), we have \(GH=\frac{4}{3}\times ZY\). Since \(ZY = 2\), then \(GH=\frac{4}{3}\times2=\frac{8}{3}\).

Answer:

\(FI=\frac{8}{3}\), \(GH=\frac{8}{3}\)