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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Question
![**Triangle Side (LW1)**
**Task:** Use the side-splitter theorem to solve for x in the triangle below.
**Diagram Explanation:**
The diagram depicts a triangle with one of its sides split into two segments. Here's a breakdown of the elements in the diagram:
- A triangle with one side divided into parts is shown.
- The segments of the triangle are labeled with the following lengths:
- The left segment of the triangle, which is denoted by \( x \).
- The lower left segment is 33 units long.
- The right segment is 12 units long.
- The lower right segment is 11 units long.
The side-splitter theorem can be used to solve for the unknown value \( x \). This theorem states that if a line parallel to one side of a triangle intersects the other two sides, it divides those sides proportionally.
To illustrate:
\[
\frac{x}{33} = \frac{12}{11}
\]
Solving this proportion will yield the value of \( x\).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F61c86ddb-00aa-4043-ac36-ebc52fad487f%2F216181bf-b4f5-4c9a-b25d-54c205ae6c81%2F2hx32z_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Triangle Side (LW1)**
**Task:** Use the side-splitter theorem to solve for x in the triangle below.
**Diagram Explanation:**
The diagram depicts a triangle with one of its sides split into two segments. Here's a breakdown of the elements in the diagram:
- A triangle with one side divided into parts is shown.
- The segments of the triangle are labeled with the following lengths:
- The left segment of the triangle, which is denoted by \( x \).
- The lower left segment is 33 units long.
- The right segment is 12 units long.
- The lower right segment is 11 units long.
The side-splitter theorem can be used to solve for the unknown value \( x \). This theorem states that if a line parallel to one side of a triangle intersects the other two sides, it divides those sides proportionally.
To illustrate:
\[
\frac{x}{33} = \frac{12}{11}
\]
Solving this proportion will yield the value of \( x\).
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