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
Related questions
Question
Part A: IG=27, Find CI
Part B: In △RST,X△RST,X is the centroid. If SX=14,SX=14, find XWXW and SW.
Transcribed Image Text:**Problem Statement:**
If \( IG = 27 \), find \( CI \).
**Diagram Explanation:**
The diagram is a geometric figure consisting of several connected triangles sharing some common points. Here are the important points and lengths:
- Points: The diagram includes points labeled as \( D, E, F, G, I, \) and \( C \).
- Segments: The following segments and their lengths are indicated:
- \( DG = 24 \)
- \( GE = 24 \)
- \( EF = 11 \)
- \( FC = 38 \)
- \( FI = 17 \)
- \( IE = 38 \)
- \( IG = 27 \) (as given)
- \( DF = 45 \)
- \( DC = 45 \)
The segments appear to connect to form triangles and quadrilaterals within the figure.
The problem requires finding the length of segment \( CI \).
**Answer Box:**
The solution to find \( CI \) would involve using geometric properties, such as congruent triangles or other relationships within the given diagram, potentially using the known lengths. However, the actual calculation or answer is not provided in the image.
![In \(\triangle RST\), \(X\) is the centroid. If \(SX = 14\), find \(XW\) and \(SW\).
**Diagram Explanation:**
The diagram shows triangle \(RST\) with centroid \(X\), and points \(U\), \(V\), and \(W\) on segments \(RS\), \(ST\), and \(RT\) respectively. The centroid \(X\) divides the medians of the triangle in a 2:1 ratio.
Since \(SX = 14\), using the centroid property:
- \(XW = \frac{1}{3} \times SW\)
- \(SW = 21\) (because \(SX\) is \( \frac{2}{3} \) of \(SW\), making \(SW = \frac{14 \times 3}{2}\))
- Therefore, \(XW = \frac{1}{3} \times 21 = 7\)
\[
\begin{align*}
XW &= \boxed{7} \\
SW &= \boxed{21}
\end{align*}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F961577a5-40e5-4c8d-9cf2-155d7db9de02%2F6fbb4584-13ba-40e7-8ecb-b57f9877502b%2Frlda3e7_processed.png&w=3840&q=75)
Transcribed Image Text:In \(\triangle RST\), \(X\) is the centroid. If \(SX = 14\), find \(XW\) and \(SW\).
**Diagram Explanation:**
The diagram shows triangle \(RST\) with centroid \(X\), and points \(U\), \(V\), and \(W\) on segments \(RS\), \(ST\), and \(RT\) respectively. The centroid \(X\) divides the medians of the triangle in a 2:1 ratio.
Since \(SX = 14\), using the centroid property:
- \(XW = \frac{1}{3} \times SW\)
- \(SW = 21\) (because \(SX\) is \( \frac{2}{3} \) of \(SW\), making \(SW = \frac{14 \times 3}{2}\))
- Therefore, \(XW = \frac{1}{3} \times 21 = 7\)
\[
\begin{align*}
XW &= \boxed{7} \\
SW &= \boxed{21}
\end{align*}
\]
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