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

ankarskogC 2021-02-26 Answered
To prove:The extended proportions that are needed to prove $\mathrm{△}RST\sim \mathrm{△}XYZ$ by the SSS similarity theorem.
Given $\mathrm{△}RST,\mathrm{△}XYZ$ are two triangles.
You can still ask an expert for help

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it

## Expert Answer

Theodore Schwartz
Answered 2021-02-27 Author has 99 answers
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:
$\frac{RS}{XY}=\frac{ST}{YZ}=\frac{RT}{XZ}$
Hence, theratios of $\frac{RS}{XY},\frac{ST}{YZ}\phantom{\rule{1em}{0ex}}\text{and}\phantom{\rule{1em}{0ex}}\frac{RT}{XZ}$ must be equal to prove $\mathrm{△}RST\sim \mathrm{△}XYZ$ by SSS similarity theorem.
###### Not exactly what you’re looking for?

Expert Community at Your Service

• Live experts 24/7
• Questions are typically answered in as fast as 30 minutes
• Personalized clear answers

Solve your problem for the price of one coffee

• Available 24/7
• Math expert for every subject
• Pay only if we can solve it