Calculation:

SSS theorem for similarity states that the ratios of sides of one triangle to the corresponding triangle’s sides must be equal.

In triangle RST and XYZ,

Consider the ratios of sides as follows:

\(\displaystyle\frac{{{R}{S}}}{{{X}{Y}}}=\frac{{{S}{T}}}{{{Y}{Z}}}=\frac{{{R}{T}}}{{{X}{Z}}}\)

Hence, theratios of \(\displaystyle\frac{{{R}{S}}}{{{X}{Y}}},\frac{{{S}{T}}}{{{Y}{Z}}}{\quad\text{and}\quad}\frac{{{R}{T}}}{{{X}{Z}}}\) must be equal to prove \(\displaystyle\triangle{R}{S}{T}\sim\triangle{X}{Y}{Z}\) by SSS similarity theorem.

SSS theorem for similarity states that the ratios of sides of one triangle to the corresponding triangle’s sides must be equal.

In triangle RST and XYZ,

Consider the ratios of sides as follows:

\(\displaystyle\frac{{{R}{S}}}{{{X}{Y}}}=\frac{{{S}{T}}}{{{Y}{Z}}}=\frac{{{R}{T}}}{{{X}{Z}}}\)

Hence, theratios of \(\displaystyle\frac{{{R}{S}}}{{{X}{Y}}},\frac{{{S}{T}}}{{{Y}{Z}}}{\quad\text{and}\quad}\frac{{{R}{T}}}{{{X}{Z}}}\) must be equal to prove \(\displaystyle\triangle{R}{S}{T}\sim\triangle{X}{Y}{Z}\) by SSS similarity theorem.