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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![**Problem: Properties of Parallelograms**
**Objective:**
Given:
- \( FH = 2v - 75 \)
- \( FJ = v - 28 \)
Find the value of \( v \) in rectangle \( GHIJ \).
**Diagram Explanation:**
The image shows a parallelogram \( GHIJ \) with a diagonal \( HFJ \). Points \( G, H, I, \) and \( J \) are vertices of the rectangle. The diagonal divides the rectangle into two congruent triangles.
**Solution Steps:**
1. Since \( GHIJ \) is a rectangle, the diagonals intersect at the midpoint and are equal in length.
2. Apply the property of the rectangle that the diagonals are equal:
\[
FH = FJ
\]
3. Use given expressions:
\[
2v - 75 = v - 28
\]
4. Solve for \( v \):
\[
2v - v = 75 - 28
\]
\[
v = 47
\]
5. Therefore, the value of \( v \) is \( 47 \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F46e25c80-76d1-40fc-b8ee-938f2c7ceeae%2Ff9a63079-82b8-4b8e-b123-96646b276347%2Fc5bcis_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem: Properties of Parallelograms**
**Objective:**
Given:
- \( FH = 2v - 75 \)
- \( FJ = v - 28 \)
Find the value of \( v \) in rectangle \( GHIJ \).
**Diagram Explanation:**
The image shows a parallelogram \( GHIJ \) with a diagonal \( HFJ \). Points \( G, H, I, \) and \( J \) are vertices of the rectangle. The diagonal divides the rectangle into two congruent triangles.
**Solution Steps:**
1. Since \( GHIJ \) is a rectangle, the diagonals intersect at the midpoint and are equal in length.
2. Apply the property of the rectangle that the diagonals are equal:
\[
FH = FJ
\]
3. Use given expressions:
\[
2v - 75 = v - 28
\]
4. Solve for \( v \):
\[
2v - v = 75 - 28
\]
\[
v = 47
\]
5. Therefore, the value of \( v \) is \( 47 \).
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