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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![### Rectangle and Diagonals Problem
The picture below shows a rectangle and its diagonals. If \( ED = 20 \), what are the lengths of \( EG \) and \( DH \)?
- \( EG = \) 40
- \( DH = \underline{\hspace{2cm}} \)
#### Explanation of the Diagram:
1. **Vertices of the Rectangle:**
- The rectangle is labeled with vertices \( E, F, G, \) and \( H \), where \( E \) is the top-left corner, \( F \) is the top-right corner, \( H \) is the bottom-left corner, and \( G \) is the bottom-right corner.
2. **Diagonals of the Rectangle:**
- The diagonals \( EG \) and \( FH \) are illustrated with dashed lines.
- The point \( D \) is marked as the intersection of the two diagonals.
3. **Given Information:**
- The length of the segment \( ED \) is given as 20.
- The length of the entire diagonal \( EG \) is given as 40.
Since \( D \) is the midpoint of \( EG \) (because diagonals of a rectangle bisect each other), it implies:
\[ ED = \frac{EG}{2} \]
Given \( EG = 40 \):
\[ ED = \frac{40}{2} = 20 \]
So, the given value of \( ED = 20 \) is consistent with the length of \( EG \).
Next, we need to confirm the length of diagonal \( DH \). In a rectangle, the diagonals are equal in length. Therefore:
\[ DH = EG \]
Hence, \( DH = 40 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3507dd34-356a-4022-bbb7-0af3373e7007%2F4d469897-de89-42d8-ba1c-a7dc9fdac692%2Fkb4149_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Rectangle and Diagonals Problem
The picture below shows a rectangle and its diagonals. If \( ED = 20 \), what are the lengths of \( EG \) and \( DH \)?
- \( EG = \) 40
- \( DH = \underline{\hspace{2cm}} \)
#### Explanation of the Diagram:
1. **Vertices of the Rectangle:**
- The rectangle is labeled with vertices \( E, F, G, \) and \( H \), where \( E \) is the top-left corner, \( F \) is the top-right corner, \( H \) is the bottom-left corner, and \( G \) is the bottom-right corner.
2. **Diagonals of the Rectangle:**
- The diagonals \( EG \) and \( FH \) are illustrated with dashed lines.
- The point \( D \) is marked as the intersection of the two diagonals.
3. **Given Information:**
- The length of the segment \( ED \) is given as 20.
- The length of the entire diagonal \( EG \) is given as 40.
Since \( D \) is the midpoint of \( EG \) (because diagonals of a rectangle bisect each other), it implies:
\[ ED = \frac{EG}{2} \]
Given \( EG = 40 \):
\[ ED = \frac{40}{2} = 20 \]
So, the given value of \( ED = 20 \) is consistent with the length of \( EG \).
Next, we need to confirm the length of diagonal \( DH \). In a rectangle, the diagonals are equal in length. Therefore:
\[ DH = EG \]
Hence, \( DH = 40 \).
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