Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN: 9781337614085
Author: Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher: Cengage,
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### Question: 1. **Are the following triangles similar? Justify your answer.** ### Diagram Explanation: The image features two triangles, △MCD and △NOL, with the following side lengths: - Triangle △MCD: - MC = 12 - CD = 6 - DM = 14 - Triangle △NOL: - NO = 49 - OL = 21 - LN = 40 The task is to determine if these two triangles are similar. In geometry, two triangles are similar if their corresponding angles are equal and the lengths of corresponding sides are proportional. The concept of similarity can be verified using criteria such as Angle-Angle (AA), Side-Side-Side (SSS), or Side-Angle-Side (SAS). ### Steps to Determine Similarity: 1. **Check for Proportional Sides:** Compare the ratios of the corresponding sides: - MC/NO = 12/49 - CD/OL = 6/21 = 2/7 - DM/LN = 14/40 = 7/20 2. **Evaluate Similarity Criteria:** Since none of the side ratios are equal, △MCD and △NOL do not meet the Side-Side-Side (SSS) criterion for similarity. Additionally, without any information about their angles or other equal side ratios, other similarity criteria also cannot be conclusively applied. ### Conclusion: The triangles △MCD and △NOL are not similar based on the information provided. The side lengths do not form consistent proportional ratios across the corresponding sides.
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Transcribed Image Text:### Question: 1. **Are the following triangles similar? Justify your answer.** ### Diagram Explanation: The image features two triangles, △MCD and △NOL, with the following side lengths: - Triangle △MCD: - MC = 12 - CD = 6 - DM = 14 - Triangle △NOL: - NO = 49 - OL = 21 - LN = 40 The task is to determine if these two triangles are similar. In geometry, two triangles are similar if their corresponding angles are equal and the lengths of corresponding sides are proportional. The concept of similarity can be verified using criteria such as Angle-Angle (AA), Side-Side-Side (SSS), or Side-Angle-Side (SAS). ### Steps to Determine Similarity: 1. **Check for Proportional Sides:** Compare the ratios of the corresponding sides: - MC/NO = 12/49 - CD/OL = 6/21 = 2/7 - DM/LN = 14/40 = 7/20 2. **Evaluate Similarity Criteria:** Since none of the side ratios are equal, △MCD and △NOL do not meet the Side-Side-Side (SSS) criterion for similarity. Additionally, without any information about their angles or other equal side ratios, other similarity criteria also cannot be conclusively applied. ### Conclusion: The triangles △MCD and △NOL are not similar based on the information provided. The side lengths do not form consistent proportional ratios across the corresponding sides.
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