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
Related questions
Question
do 2, please
![### Extra Credit for the Final Exam
#### Problem 1
**Given:**
- Triangle \( \triangle ABD \)
**Task:**
- \( AD \) is the geometric mean of \( BD \) and \( DC \)
- Find \( DC \) if \( AD = 2 \sqrt{10} \) and \( BC = 16 \) (Refer to Textbook page 130)
**Solution:**
- Let \( DC = x \)
- Then, \( BD = 16 - x \)
- Since \( AD \) is the geometric mean:
\[ \frac{2\sqrt{10}}{1} = \sqrt{(16 - x)(x)} \]
\[ 40 = (16 - x) x \]
\[ x^2 - 16x + 40 = 0 \]
#### Diagrams:
1. **Triangle Diagram:**
- Triangle \( \triangle ABD \) with points labeled \( A \), \( B \), \( D \), and \( C \).
- Side \( AD \) is shown as the geometric mean of \( BD \) and \( DC \).
#### Problem 2
- **Given:**
- \( m\angle ABC = 20^\circ \)
- **Task:**
- Find \( m\angle AD \)
- Find \( m\angle BD \)
#### Diagram:
2. **Circle and Triangle Diagram:**
- Circle with points \( A \), \( B \), \( C \), and \( D \).
- \( \angle ABC \) is marked with a given value of \( 20^\circ \).
### Additional Given Information and Problems
**Given:**
- \( m\angle CFA = 78^\circ \)
- \( m\angle BAE = 24^\circ \)
**Task:**
- Find \( m\angle ABD \) and other angles.
#### Diagram:
3. **Complex Circle Diagram:**
- Circle with multiple intersecting triangles.
- Labeled points \( A \), \( B \), \( C \), \( D \), and \( E \).
- Specific angle measures and relationships provided.
#### Angles Calculation:
- Use properties of circles and triangles to calculate unknown angles.
### Explanation of Diagrams:
1. **Triangle \( \triangle ABD \)**:
- A triangle with vertices \( A \), \( B \),](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5bbe15d5-05c4-4aea-a090-ae763138d27c%2F12983fa7-f7fd-4d8d-be52-53db29c53e63%2Fydcaj3_reoriented.jpeg&w=3840&q=75)
Transcribed Image Text:### Extra Credit for the Final Exam
#### Problem 1
**Given:**
- Triangle \( \triangle ABD \)
**Task:**
- \( AD \) is the geometric mean of \( BD \) and \( DC \)
- Find \( DC \) if \( AD = 2 \sqrt{10} \) and \( BC = 16 \) (Refer to Textbook page 130)
**Solution:**
- Let \( DC = x \)
- Then, \( BD = 16 - x \)
- Since \( AD \) is the geometric mean:
\[ \frac{2\sqrt{10}}{1} = \sqrt{(16 - x)(x)} \]
\[ 40 = (16 - x) x \]
\[ x^2 - 16x + 40 = 0 \]
#### Diagrams:
1. **Triangle Diagram:**
- Triangle \( \triangle ABD \) with points labeled \( A \), \( B \), \( D \), and \( C \).
- Side \( AD \) is shown as the geometric mean of \( BD \) and \( DC \).
#### Problem 2
- **Given:**
- \( m\angle ABC = 20^\circ \)
- **Task:**
- Find \( m\angle AD \)
- Find \( m\angle BD \)
#### Diagram:
2. **Circle and Triangle Diagram:**
- Circle with points \( A \), \( B \), \( C \), and \( D \).
- \( \angle ABC \) is marked with a given value of \( 20^\circ \).
### Additional Given Information and Problems
**Given:**
- \( m\angle CFA = 78^\circ \)
- \( m\angle BAE = 24^\circ \)
**Task:**
- Find \( m\angle ABD \) and other angles.
#### Diagram:
3. **Complex Circle Diagram:**
- Circle with multiple intersecting triangles.
- Labeled points \( A \), \( B \), \( C \), \( D \), and \( E \).
- Specific angle measures and relationships provided.
#### Angles Calculation:
- Use properties of circles and triangles to calculate unknown angles.
### Explanation of Diagrams:
1. **Triangle \( \triangle ABD \)**:
- A triangle with vertices \( A \), \( B \),
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 6 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, geometry and related others by exploring similar questions and additional content below.Recommended textbooks for you
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning
Elementary Geometry For College Students, 7e
Geometry
ISBN:
9781337614085
Author:
Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:
Cengage,
Elementary Geometry for College Students
Geometry
ISBN:
9781285195698
Author:
Daniel C. Alexander, Geralyn M. Koeberlein
Publisher:
Cengage Learning