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Triangle ABC is similar to triangle PQR. Which proportion can be used to find n? R

Triangle ABC is similar to triangle PQR. Which proportion can be used to find n? R

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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**Educational Content: Understanding Similar Triangles** This exercise involves two similar triangles, \( \triangle ABC \) and \( \triangle PQR \), and the goal is to determine which proportion can be used to find the unknown side length \( n \). **Triangles Illustrated:** - **Triangle \( \triangle ABC \):** - Side \( AC = 8 \) - Side \( CB = 9 \) - Vertical height \( AB = 4 \) - **Triangle \( \triangle PQR \):** - Side \( PR = 24 \) - Side \( RQ = 12 \) - Hypotenuse represented as \( n \) **Question:** Which proportion can be used to find \( n \)? **Answer Options:** A) \( \frac{8}{9} = \frac{n}{12} \) B) \( \frac{8}{12} = \frac{n}{9} \) C) \( \frac{4}{8} = \frac{12}{n} \) D) \( \frac{4}{9} = \frac{12}{n} \) **Concept Explanation:** Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. Here, options A through D propose different proportions based on the given side lengths. To solve for \( n \), consider the corresponding sides of these similar triangles. Look for sets of corresponding sides that allow you to compute the length of \( n \) accurately by setting up equivalent ratios. Explore which option correctly maintains the proportion between \( \triangle ABC \) and \( \triangle PQR \).
Transcribed Image Text:**Educational Content: Understanding Similar Triangles** This exercise involves two similar triangles, \( \triangle ABC \) and \( \triangle PQR \), and the goal is to determine which proportion can be used to find the unknown side length \( n \). **Triangles Illustrated:** - **Triangle \( \triangle ABC \):** - Side \( AC = 8 \) - Side \( CB = 9 \) - Vertical height \( AB = 4 \) - **Triangle \( \triangle PQR \):** - Side \( PR = 24 \) - Side \( RQ = 12 \) - Hypotenuse represented as \( n \) **Question:** Which proportion can be used to find \( n \)? **Answer Options:** A) \( \frac{8}{9} = \frac{n}{12} \) B) \( \frac{8}{12} = \frac{n}{9} \) C) \( \frac{4}{8} = \frac{12}{n} \) D) \( \frac{4}{9} = \frac{12}{n} \) **Concept Explanation:** Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion. Here, options A through D propose different proportions based on the given side lengths. To solve for \( n \), consider the corresponding sides of these similar triangles. Look for sets of corresponding sides that allow you to compute the length of \( n \) accurately by setting up equivalent ratios. Explore which option correctly maintains the proportion between \( \triangle ABC \) and \( \triangle PQR \).
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