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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Ratios
A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.
Trigonometric Ratios
Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.
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If ∆ABC ≅ ∆DEF and AB = 15, BC = 20, DE = 3x - 6, then
![If \( \triangle ABC \cong \triangle DEF \) and \( AB = 15 \), \( BC = 20 \), \( DE = 3x - 6 \), then
\( x = ? \)
**Solve for \( x \)**
\( x = \) [input box]
### Explanation
In the given problem, two triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent (\(\cong\)), meaning all corresponding sides and angles are equal. The task is to find the value of \( x \).
- Given \( AB = 15 \) and \( BC = 20 \).
- \( DE = 3x - 6 \).
Since the triangles are congruent, the sides opposite congruent angles are equal. Therefore, the side \( DE \) in \( \triangle DEF \) is equal to \( AB \) in \( \triangle ABC \).
### Solving the Equation
1. Set the expressions equal: \( 15 = 3x - 6 \).
2. Solve for \( x \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65e7fdd2-c053-44ef-a2cf-e957577c7b2e%2F6488baa8-d41b-45c4-a142-d9b36a62ddda%2Fmgybyu_processed.png&w=3840&q=75)
Transcribed Image Text:If \( \triangle ABC \cong \triangle DEF \) and \( AB = 15 \), \( BC = 20 \), \( DE = 3x - 6 \), then
\( x = ? \)
**Solve for \( x \)**
\( x = \) [input box]
### Explanation
In the given problem, two triangles \( \triangle ABC \) and \( \triangle DEF \) are congruent (\(\cong\)), meaning all corresponding sides and angles are equal. The task is to find the value of \( x \).
- Given \( AB = 15 \) and \( BC = 20 \).
- \( DE = 3x - 6 \).
Since the triangles are congruent, the sides opposite congruent angles are equal. Therefore, the side \( DE \) in \( \triangle DEF \) is equal to \( AB \) in \( \triangle ABC \).
### Solving the Equation
1. Set the expressions equal: \( 15 = 3x - 6 \).
2. Solve for \( x \).
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