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 2 (1 point)
**Problem Statement:**
Find the values of \( x \) and \( y \) in the parallelogram.
**Diagram:**
A parallelogram \( ABCD \) with sides labeled as follows:
- Side \( DC \) = 24
- Side \( CB \) = 11
- Side \( AB \) = \( x - 2 \)
- Side \( DA \) = \( y \)
```
D y A
|------------------|
| |
24 | | x - 2
|------------------|
C 11 B
```
**Answer Choices:**
- **a.** \( x = 11, y = 26 \)
- **b.** \( x = 24, y = 13 \)
- **c.** \( x = 13, y = 24 \)
- **d.** \( x = 26, y = 11 \)
**Explanation:**
In a parallelogram, opposite sides are equal. Therefore:
- \( AB = CD \)
- \( AD = BC \)
By using these properties, you can solve for \( x \) and \( y \) by setting up and solving the corresponding equations based on the given lengths.
Proper steps include:
1. Stating that \( x - 2 = 24 \) (since \( AB = CD \))
2. Solving for \( x \):
\[
x - 2 = 24
\]
\[
x = 24 + 2
\]
\[
x = 26
\]
3. Stating that \( y = 11 \) (since \( DA = BC \))
Therefore, the correct answer is:
- **d.** \( x = 26, y = 11 \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9515abb1-920e-411d-9b5f-f7bc9d9dbe1f%2F69367615-c754-4657-9f7c-599f6b567724%2F611jth8_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Question 2 (1 point)
**Problem Statement:**
Find the values of \( x \) and \( y \) in the parallelogram.
**Diagram:**
A parallelogram \( ABCD \) with sides labeled as follows:
- Side \( DC \) = 24
- Side \( CB \) = 11
- Side \( AB \) = \( x - 2 \)
- Side \( DA \) = \( y \)
```
D y A
|------------------|
| |
24 | | x - 2
|------------------|
C 11 B
```
**Answer Choices:**
- **a.** \( x = 11, y = 26 \)
- **b.** \( x = 24, y = 13 \)
- **c.** \( x = 13, y = 24 \)
- **d.** \( x = 26, y = 11 \)
**Explanation:**
In a parallelogram, opposite sides are equal. Therefore:
- \( AB = CD \)
- \( AD = BC \)
By using these properties, you can solve for \( x \) and \( y \) by setting up and solving the corresponding equations based on the given lengths.
Proper steps include:
1. Stating that \( x - 2 = 24 \) (since \( AB = CD \))
2. Solving for \( x \):
\[
x - 2 = 24
\]
\[
x = 24 + 2
\]
\[
x = 26
\]
3. Stating that \( y = 11 \) (since \( DA = BC \))
Therefore, the correct answer is:
- **d.** \( x = 26, y = 11 \)
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