Question

# To prove:The extended proportions that are needed to prove /_RST ~ /_XYZ by the SSS similarity theorem. Given /_RST, /_XYZ are two triangles.

Similarity
To prove:The extended proportions that are needed to prove $$\displaystyle\triangle{R}{S}{T}\sim\triangle{X}{Y}{Z}$$ by the SSS similarity theorem.
Given $$\displaystyle\triangle{R}{S}{T},\triangle{X}{Y}{Z}$$ are two triangles.

$$\displaystyle\frac{{{R}{S}}}{{{X}{Y}}}=\frac{{{S}{T}}}{{{Y}{Z}}}=\frac{{{R}{T}}}{{{X}{Z}}}$$
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.