Given

ankarskogC
2021-02-26
Answered

To prove:The extended proportions that are needed to prove $\mathrm{\u25b3}RST\sim \mathrm{\u25b3}XYZ$ by the SSS similarity theorem.

Given$\mathrm{\u25b3}RST,\mathrm{\u25b3}XYZ$ are two triangles.

Given

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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$\frac{RS}{XY},\frac{ST}{YZ}{\textstyle \phantom{\rule{1em}{0ex}}}\text{and}{\textstyle \phantom{\rule{1em}{0ex}}}\frac{RT}{XZ}$ must be equal to prove $\mathrm{\u25b3}RST\sim \mathrm{\u25b3}XYZ$ 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:

Hence, theratios of

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