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**Example 5: Are the triangles similar? If so, write a similarity statement.** The image shows two triangles labeled \(\triangle RST\) and \(\triangle XYZ\). - **Triangle \(\triangle RST\):** - Side \(RS = 6\) - Side \(ST = 8\) - Side \(RT = 12\) - **Triangle \(\triangle XYZ\):** - Side \(XY = 3\) - Side \(YZ = 4\) - Side \(XZ = 5\) **Analysis:** To determine if the triangles are similar, compare the ratios of their corresponding sides. - \( \frac{RS}{XY} = \frac{6}{3} = 2 \) - \( \frac{ST}{YZ} = \frac{8}{4} = 2 \) - \( \frac{RT}{XZ} = \frac{12}{5} \neq 2 \) Since all corresponding sides are not proportional, the triangles are not similar. **Conclusion:** The triangles \(\triangle RST\) and \(\triangle XYZ\) are not similar.

**Example 5: Are the triangles similar? If so, write a similarity statement.** The image shows two triangles labeled \(\triangle RST\) and \(\triangle XYZ\). - **Triangle \(\triangle RST\):** - Side \(RS = 6\) - Side \(ST = 8\) - Side \(RT = 12\) - **Triangle \(\triangle XYZ\):** - Side \(XY = 3\) - Side \(YZ = 4\) - Side \(XZ = 5\) **Analysis:** To determine if the triangles are similar, compare the ratios of their corresponding sides. - \( \frac{RS}{XY} = \frac{6}{3} = 2 \) - \( \frac{ST}{YZ} = \frac{8}{4} = 2 \) - \( \frac{RT}{XZ} = \frac{12}{5} \neq 2 \) Since all corresponding sides are not proportional, the triangles are not similar. **Conclusion:** The triangles \(\triangle RST\) and \(\triangle XYZ\) are not similar.

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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**Example 5: Are the triangles similar? If so, write a similarity statement.** The image shows two triangles labeled \(\triangle RST\) and \(\triangle XYZ\). - **Triangle \(\triangle RST\):** - Side \(RS = 6\) - Side \(ST = 8\) - Side \(RT = 12\) - **Triangle \(\triangle XYZ\):** - Side \(XY = 3\) - Side \(YZ = 4\) - Side \(XZ = 5\) **Analysis:** To determine if the triangles are similar, compare the ratios of their corresponding sides. - \( \frac{RS}{XY} = \frac{6}{3} = 2 \) - \( \frac{ST}{YZ} = \frac{8}{4} = 2 \) - \( \frac{RT}{XZ} = \frac{12}{5} \neq 2 \) Since all corresponding sides are not proportional, the triangles are not similar. **Conclusion:** The triangles \(\triangle RST\) and \(\triangle XYZ\) are not similar.
Transcribed Image Text:**Example 5: Are the triangles similar? If so, write a similarity statement.** The image shows two triangles labeled \(\triangle RST\) and \(\triangle XYZ\). - **Triangle \(\triangle RST\):** - Side \(RS = 6\) - Side \(ST = 8\) - Side \(RT = 12\) - **Triangle \(\triangle XYZ\):** - Side \(XY = 3\) - Side \(YZ = 4\) - Side \(XZ = 5\) **Analysis:** To determine if the triangles are similar, compare the ratios of their corresponding sides. - \( \frac{RS}{XY} = \frac{6}{3} = 2 \) - \( \frac{ST}{YZ} = \frac{8}{4} = 2 \) - \( \frac{RT}{XZ} = \frac{12}{5} \neq 2 \) Since all corresponding sides are not proportional, the triangles are not similar. **Conclusion:** The triangles \(\triangle RST\) and \(\triangle XYZ\) are not similar.
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