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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![# Geometry: Rhombus ABCD Analysis
**Topic: Geometry**
**Course: Geometry 2**
---
### Use Rhombus ABCD to answer the following questions
Given the following:
- \( AD = 10 \)
- \( AC = 16 \)
- \( m \angle ABC = 130^\circ \)
#### Diagram Description:
A rhombus \(ABCD\) is depicted with diagonals \(AC\) and \(BD\) intersecting at point \(W\). The angles are as follows:
- \(\angle ABC = 130^\circ\)
The diagonals of the rhombus intersect at right angles (90 degrees) at \(W\), forming four right-angled triangles.
### Questions:
1. **AB =**
- Answer: 10
2. **CW =**
- Answer: 8
3. **The measure of angle \(BAD\) =**
- Answer: [Fill in answer in degrees]
4. **The measure of angle \(CDB\) =**
- Answer: [Fill in answer in degrees]
5. **The measure of angle \(DWA\) =**
- Answer: [Fill in answer in degrees]
6. **The measure of angle \(WCD\) =**
- Answer: [Fill in answer in degrees]
### Explanation:
When working with the given angles and properties of the rhombus, apply the following geometrical properties:
- **Properties of a rhombus**: All sides are equal, and the diagonals bisect each other at right angles.
- Diagonals of a rhombus split it into four right triangles.
### Steps to Solve the Missing Angles:
1. **Angle \(BAD\)**:
- Since \(\angle ABC\) is 130 degrees and diagonals bisect each other, \(\angle BCD = 130^\circ\).
- \( \angle BAD = 180^\circ - 130^\circ = 50^\circ\).
2. **Angle \(CDB\)**:
- Since rhombus diagonals form 90 degrees at the intersection,
- \( \angle CDA = 90^\circ\).
3. **Angle \(DWA\)**:
- Since point \(W\) is the intersection of diagonals, forming right angles,
- \( \angle DWA = 90^\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F01b580fa-011d-4ada-be68-942e2d4e7c99%2F0e594218-e9a2-41b0-9bed-12e6de26c177%2F7y6d65r_processed.jpeg&w=3840&q=75)
Transcribed Image Text:# Geometry: Rhombus ABCD Analysis
**Topic: Geometry**
**Course: Geometry 2**
---
### Use Rhombus ABCD to answer the following questions
Given the following:
- \( AD = 10 \)
- \( AC = 16 \)
- \( m \angle ABC = 130^\circ \)
#### Diagram Description:
A rhombus \(ABCD\) is depicted with diagonals \(AC\) and \(BD\) intersecting at point \(W\). The angles are as follows:
- \(\angle ABC = 130^\circ\)
The diagonals of the rhombus intersect at right angles (90 degrees) at \(W\), forming four right-angled triangles.
### Questions:
1. **AB =**
- Answer: 10
2. **CW =**
- Answer: 8
3. **The measure of angle \(BAD\) =**
- Answer: [Fill in answer in degrees]
4. **The measure of angle \(CDB\) =**
- Answer: [Fill in answer in degrees]
5. **The measure of angle \(DWA\) =**
- Answer: [Fill in answer in degrees]
6. **The measure of angle \(WCD\) =**
- Answer: [Fill in answer in degrees]
### Explanation:
When working with the given angles and properties of the rhombus, apply the following geometrical properties:
- **Properties of a rhombus**: All sides are equal, and the diagonals bisect each other at right angles.
- Diagonals of a rhombus split it into four right triangles.
### Steps to Solve the Missing Angles:
1. **Angle \(BAD\)**:
- Since \(\angle ABC\) is 130 degrees and diagonals bisect each other, \(\angle BCD = 130^\circ\).
- \( \angle BAD = 180^\circ - 130^\circ = 50^\circ\).
2. **Angle \(CDB\)**:
- Since rhombus diagonals form 90 degrees at the intersection,
- \( \angle CDA = 90^\circ\).
3. **Angle \(DWA\)**:
- Since point \(W\) is the intersection of diagonals, forming right angles,
- \( \angle DWA = 90^\
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