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Are the two triangles similar? 18 20 16 12 15 24

Are the two triangles similar? 18 20 16 12 15 24

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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### Transcription for Educational Use **Question:** Are the two triangles similar? **Diagrams:** - **First Triangle:** - Sides: 20, 16, 24 - It shows angle markers indicating possible congruency with the second triangle. - **Second Triangle:** - Sides: 18, 12, 15 - It shows angle markers that correspond with those of the first triangle, indicating possible angle congruency. **Your answer:** - ○ Yes - ○ No ### Explanation of Triangles - **Similarity Criteria:** - Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. - **Examining Side Ratios:** - Compare the ratio of corresponding sides: - \( \frac{20}{18} \), \( \frac{16}{12} \), \( \frac{24}{15} \) - Check if these ratios are equivalent. - **Conclusion:** - If the ratios are equal, the triangles are similar. If not, they are not similar. This activity requires understanding and applying the conditions for triangle similarity using side ratios and angle congruency.
Transcribed Image Text:### Transcription for Educational Use **Question:** Are the two triangles similar? **Diagrams:** - **First Triangle:** - Sides: 20, 16, 24 - It shows angle markers indicating possible congruency with the second triangle. - **Second Triangle:** - Sides: 18, 12, 15 - It shows angle markers that correspond with those of the first triangle, indicating possible angle congruency. **Your answer:** - ○ Yes - ○ No ### Explanation of Triangles - **Similarity Criteria:** - Two triangles are similar if their corresponding angles are equal and their corresponding sides are proportional. - **Examining Side Ratios:** - Compare the ratio of corresponding sides: - \( \frac{20}{18} \), \( \frac{16}{12} \), \( \frac{24}{15} \) - Check if these ratios are equivalent. - **Conclusion:** - If the ratios are equal, the triangles are similar. If not, they are not similar. This activity requires understanding and applying the conditions for triangle similarity using side ratios and angle congruency.
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Step 1

Similar triangles are two or more triangles with the 

  • same shape,
  • equal pair of corresponding angles, and
  • same ratio of the corresponding sides

Geometry homework question answer, step 1, image 1

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