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 19: Geometry Problem
#### Instructions:
DE is a midsegment of triangle ABC. Find the value of \( x \).
#### Diagram:
- The figure shows triangle ABC.
- Points D and E are located on the sides AB and AC respectively, such that DE is parallel to BC and D is the midpoint of AB, and E is the midpoint of AC.
- Segment DE is labeled with a length of 5 units.
- The segment BC is labeled with a length of \( x \) units.
#### Answer Choices:
- 20
- 15
- 10
- 5
#### Detailed Solution:
In the context of triangle ABC, since DE is a midsegment, it is parallel to BC and its length is half the length of BC. This means:
\[ DE = \frac{1}{2}BC \]
Given that the length of DE is 5 units, we can set up the equation:
\[ 5 = \frac{1}{2}x \]
To solve for \( x \):
\[ 5 \times 2 = x \]
\[ x = 10 \]
#### Conclusion:
The value of \( x \) is 10.
#### Correct Answer:
- 10](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4bd06414-f1f6-4940-956f-9c39fe649804%2F4f0fb634-83aa-4d05-b91e-e7b95fab3fbb%2Fhw2d52r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 19: Geometry Problem
#### Instructions:
DE is a midsegment of triangle ABC. Find the value of \( x \).
#### Diagram:
- The figure shows triangle ABC.
- Points D and E are located on the sides AB and AC respectively, such that DE is parallel to BC and D is the midpoint of AB, and E is the midpoint of AC.
- Segment DE is labeled with a length of 5 units.
- The segment BC is labeled with a length of \( x \) units.
#### Answer Choices:
- 20
- 15
- 10
- 5
#### Detailed Solution:
In the context of triangle ABC, since DE is a midsegment, it is parallel to BC and its length is half the length of BC. This means:
\[ DE = \frac{1}{2}BC \]
Given that the length of DE is 5 units, we can set up the equation:
\[ 5 = \frac{1}{2}x \]
To solve for \( x \):
\[ 5 \times 2 = x \]
\[ x = 10 \]
#### Conclusion:
The value of \( x \) is 10.
#### Correct Answer:
- 10
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Cengage,
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9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
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Cengage Learning