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: Triangle Rotation and Perimeter Calculation**
**Problem:**
Triangle △ABC is rotated 135° about point S to create △A'B'C'.
**Diagram Analysis:**
The original triangle △ABC has the following properties:
- Vertex A with an angle of 20°.
- Side AB with a length of 5.8 units.
- Side BC with a length of 5.1 units.
After rotation around point S:
- Vertex B' has an angle of 101°.
- Side A'B' has a length of 5.8 units.
- Side B'C' has a length of 2 units.
**Question:**
What is the perimeter of △ABC?
**Solution Approach:**
To calculate the perimeter of △ABC, sum the lengths of all its sides:
- AB = 5.8 units.
- BC = 5.1 units.
- CA = unknown.
Since the rotation does not affect the lengths of the sides of the triangle, CA in △ABC is equal to C'A' in △A'B'C', which we find through geometric interpretation or additional given information in a broader context.
The final solution involves adding all sides:
\[ \text{Perimeter of } △ABC = AB + BC + CA \]
**Detailed Step-by-Step Solution:**
1. Identify the given sides of △ABC and fill in the missing length if necessary.
2. Sum the lengths of all sides.
Note: The solution would typically include all necessary length measurements and any required supplementary geometric principles to find missing side lengths.
---
This content provides an example of a geometric transformation (rotation) problem and outlines the steps required to solve for the perimeter of a given triangle.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F248cf66c-a0cc-4186-b46a-753c4174a8e6%2F595f83d5-688e-49fb-b946-31257f8188e5%2Fmc5q4x_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Geometry: Triangle Rotation and Perimeter Calculation**
**Problem:**
Triangle △ABC is rotated 135° about point S to create △A'B'C'.
**Diagram Analysis:**
The original triangle △ABC has the following properties:
- Vertex A with an angle of 20°.
- Side AB with a length of 5.8 units.
- Side BC with a length of 5.1 units.
After rotation around point S:
- Vertex B' has an angle of 101°.
- Side A'B' has a length of 5.8 units.
- Side B'C' has a length of 2 units.
**Question:**
What is the perimeter of △ABC?
**Solution Approach:**
To calculate the perimeter of △ABC, sum the lengths of all its sides:
- AB = 5.8 units.
- BC = 5.1 units.
- CA = unknown.
Since the rotation does not affect the lengths of the sides of the triangle, CA in △ABC is equal to C'A' in △A'B'C', which we find through geometric interpretation or additional given information in a broader context.
The final solution involves adding all sides:
\[ \text{Perimeter of } △ABC = AB + BC + CA \]
**Detailed Step-by-Step Solution:**
1. Identify the given sides of △ABC and fill in the missing length if necessary.
2. Sum the lengths of all sides.
Note: The solution would typically include all necessary length measurements and any required supplementary geometric principles to find missing side lengths.
---
This content provides an example of a geometric transformation (rotation) problem and outlines the steps required to solve for the perimeter of a given triangle.
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