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
![### Transcription and Diagram Explanation for Educational Use
#### Problem Statement
Triangle \( DEF \) is similar to triangle \( ABC \).
#### Diagram Description
- **Triangle ABC**:
- \( \angle A \) is labeled as 40°.
- \( AB \) is the side adjacent to \( \angle A \).
- \( BC \) is the base of the triangle, forming a right angle with \( AB \).
- **Triangle DEF**:
- This triangle is not labeled with any angles but is similar to triangle \( ABC \), suggesting that the corresponding angles are equal.
#### Question
What is the measure, in degrees, of \( \angle F \)? Explain how you know.
#### Explanation
Since triangle \( DEF \) is similar to triangle \( ABC \), the corresponding angles in similar triangles are equal. This means:
- \( \angle F \) in triangle \( DEF \) is equal to \( \angle C \) in triangle \( ABC \).
To find \( \angle F \):
- The sum of angles in a triangle is always 180°.
- Triangle \( ABC \) has a known angle of 40° (\( \angle A \)) and a right angle (\( \angle B \) as 90°), so:
\[
\angle C = 180° - 90° - 40° = 50°
\]
Therefore, \( \angle F = 50° \).
### Conclusion
The measure of \( \angle F \) is 50 degrees.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78f1df89-f554-48ce-b324-2832bb39fc25%2F81145401-fb00-4fab-947a-aa21c71413c7%2Fonhr2bc_processed.png&w=3840&q=75)
Transcribed Image Text:### Transcription and Diagram Explanation for Educational Use
#### Problem Statement
Triangle \( DEF \) is similar to triangle \( ABC \).
#### Diagram Description
- **Triangle ABC**:
- \( \angle A \) is labeled as 40°.
- \( AB \) is the side adjacent to \( \angle A \).
- \( BC \) is the base of the triangle, forming a right angle with \( AB \).
- **Triangle DEF**:
- This triangle is not labeled with any angles but is similar to triangle \( ABC \), suggesting that the corresponding angles are equal.
#### Question
What is the measure, in degrees, of \( \angle F \)? Explain how you know.
#### Explanation
Since triangle \( DEF \) is similar to triangle \( ABC \), the corresponding angles in similar triangles are equal. This means:
- \( \angle F \) in triangle \( DEF \) is equal to \( \angle C \) in triangle \( ABC \).
To find \( \angle F \):
- The sum of angles in a triangle is always 180°.
- Triangle \( ABC \) has a known angle of 40° (\( \angle A \)) and a right angle (\( \angle B \) as 90°), so:
\[
\angle C = 180° - 90° - 40° = 50°
\]
Therefore, \( \angle F = 50° \).
### Conclusion
The measure of \( \angle F \) is 50 degrees.
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