Question

1. name all similar relationships.

Explanation:

Step1: Calculate the ratios of corresponding sides for each pair of rectangles

For \(R_1\) and \(R_2\):
\(\frac{10}{5} = 2\), \(\frac{4}{2}=2\)
For \(R_1\) and \(R_3\):
\(\frac{10}{1.25}=8\), \(\frac{4}{3.125}=\frac{4\times8}{3.125\times8}=\frac{32}{25} = 1.28\)
For \(R_1\) and \(R_4\):
\(\frac{10}{3}=\frac{10}{3}\), \(\frac{4}{7.5}=\frac{4\times2}{7.5\times2}=\frac{8}{15}\)
For \(R_2\) and \(R_3\):
\(\frac{5}{1.25} = 4\), \(\frac{2}{3.125}=\frac{2\times8}{3.125\times8}=\frac{16}{25}=0.64\)
For \(R_2\) and \(R_4\):
\(\frac{5}{3}=\frac{5}{3}\), \(\frac{2}{7.5}=\frac{2\times2}{7.5\times2}=\frac{4}{15}\)
For \(R_3\) and \(R_4\):
\(\frac{1.25}{3}=\frac{1.25\times4}{3\times4}=\frac{5}{12}\), \(\frac{3.125}{7.5}=\frac{3.125\times8}{7.5\times8}=\frac{25}{60}=\frac{5}{12}\)

Answer:

\(R_1\sim R_2\), \(R_3\sim R_4\)