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Find the missing side length d given AABC ~ADEF. f = 16 e = 8 d a =4 A C b.

Find the missing side length d given AABC ~ADEF. f = 16 e = 8 d a =4 A C b.

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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**Find the missing side length \( d \) given \( \triangle ABC \sim \triangle DEF \).** ### Diagram Explanation: 1. **Triangle \( \triangle ABC \):** - Right triangle with vertex \( C \). - Side \( a = 4 \) (adjacent to angle at vertex \( B \)). - Hypotenuse \( c = 8 \). - Opposite side \( b \). 2. **Triangle \( \triangle DEF \):** - Right triangle with vertex \( F \). - Side \( d \) (corresponding to side \( a \) in \( \triangle ABC \)). - Hypotenuse \( f = 16 \). - Opposite side \( e \). ### Problem Context: These triangles are similar (\( \triangle ABC \sim \triangle DEF \)), meaning their corresponding angles are equal, and their sides are proportional. The task is to find the value of side length \( d \) in triangle \( \triangle DEF \). Use the proportional relationships between the sides of the similar triangles.
Transcribed Image Text:**Find the missing side length \( d \) given \( \triangle ABC \sim \triangle DEF \).** ### Diagram Explanation: 1. **Triangle \( \triangle ABC \):** - Right triangle with vertex \( C \). - Side \( a = 4 \) (adjacent to angle at vertex \( B \)). - Hypotenuse \( c = 8 \). - Opposite side \( b \). 2. **Triangle \( \triangle DEF \):** - Right triangle with vertex \( F \). - Side \( d \) (corresponding to side \( a \) in \( \triangle ABC \)). - Hypotenuse \( f = 16 \). - Opposite side \( e \). ### Problem Context: These triangles are similar (\( \triangle ABC \sim \triangle DEF \)), meaning their corresponding angles are equal, and their sides are proportional. The task is to find the value of side length \( d \) in triangle \( \triangle DEF \). Use the proportional relationships between the sides of the similar triangles.
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