メ 19. DE is a midsegment of triangle ABC. Find the value of x. * D 5. 2. O 5 O 10 O 15 O 20

Elementary Geometry For College Students, 7e
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ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
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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
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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