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
![**Topic: Angle Relationships and Equations in Geometry**
---
**Section 1.111: Examine the diagram below. Which diagram(s) are possible? Which are impossible? Justify each conclusion.**
**a)**
A right triangle with one leg measuring 20m and another leg measuring 5m.
**Labeling on the triangle:**
- 20m is the hypotenuse
- 5m is one leg
- The other leg is 11m
**Justification:**
It is written in the image notes that this configuration is "Not possible." The reasoning given is "Wrong measures. It is not true." The triangle inequality theorem or the Pythagorean theorem can be used to verify this.
**b)**
A triangle with three interior angles labeled:
- 96°
- \(2x\)
- \(x + 12\)
**Justification:**
To determine if the triangle is possible:
\[ 96° + 2x + (x + 12°) = 180° \]
\[ 96° + 3x + 12° = 180° \]
\[ 3x + 108° = 180° \]
\[ 3x = 72° \]
\[ x = 24° \]
Thus, the angles are:
\[ 96°, 48°, 36° \]
This confirms the triangle is possible.
**c)**
A triangle with three interior angles labeled:
- 80°
- 40°
- \(x\)
**Justification:**
To determine if the triangle is possible:
\[ 80° + 40° + x = 180° \]
\[ x = 60° \]
Thus, the angles are:
\[ 80°, 40°, 60° \]
This confirms the triangle is possible.
---
**Section 1.112: Copy and complete each of the Diamond Problems below.**
**a) Diamond Problem:**
- Multiplication (product): 6 × 8 = 48
- Sum: 6 + 8 = 14
**b) Diamond Problem:**
- Multiplication (product): 3 × 7 = 21
- Sum: 3 + 7 = 10
**Section 1.113: Examine the angle pair relationships in the diagram below. Then write and solve equations for x and y if \( \angle 1 + \angle 2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcba8a4b3-85c1-4978-9a94-0dae7d7e7cc0%2Ff28b5221-a242-4e8d-b52f-86e36e2d10c5%2F51o5ez5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Topic: Angle Relationships and Equations in Geometry**
---
**Section 1.111: Examine the diagram below. Which diagram(s) are possible? Which are impossible? Justify each conclusion.**
**a)**
A right triangle with one leg measuring 20m and another leg measuring 5m.
**Labeling on the triangle:**
- 20m is the hypotenuse
- 5m is one leg
- The other leg is 11m
**Justification:**
It is written in the image notes that this configuration is "Not possible." The reasoning given is "Wrong measures. It is not true." The triangle inequality theorem or the Pythagorean theorem can be used to verify this.
**b)**
A triangle with three interior angles labeled:
- 96°
- \(2x\)
- \(x + 12\)
**Justification:**
To determine if the triangle is possible:
\[ 96° + 2x + (x + 12°) = 180° \]
\[ 96° + 3x + 12° = 180° \]
\[ 3x + 108° = 180° \]
\[ 3x = 72° \]
\[ x = 24° \]
Thus, the angles are:
\[ 96°, 48°, 36° \]
This confirms the triangle is possible.
**c)**
A triangle with three interior angles labeled:
- 80°
- 40°
- \(x\)
**Justification:**
To determine if the triangle is possible:
\[ 80° + 40° + x = 180° \]
\[ x = 60° \]
Thus, the angles are:
\[ 80°, 40°, 60° \]
This confirms the triangle is possible.
---
**Section 1.112: Copy and complete each of the Diamond Problems below.**
**a) Diamond Problem:**
- Multiplication (product): 6 × 8 = 48
- Sum: 6 + 8 = 14
**b) Diamond Problem:**
- Multiplication (product): 3 × 7 = 21
- Sum: 3 + 7 = 10
**Section 1.113: Examine the angle pair relationships in the diagram below. Then write and solve equations for x and y if \( \angle 1 + \angle 2
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