Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![**Question 5**
How many symmetries (number of each type: line, rotation, etc.) does a regular hexagon have? Explain.
[Image of a regular hexagon]
**Explanation:**
A regular hexagon has a total of 12 symmetries. These symmetries include:
1. **Rotational Symmetries**:
- The hexagon can be rotated around its center at angles of 0°, 60°, 120°, 180°, 240°, and 300°. This gives us 6 rotational symmetries.
2. **Reflectional Symmetries**:
- The hexagon can be reflected along 6 different axes of symmetry: each passing through one vertex and the midpoint of the opposite side, or each passing through the midpoints of opposite sides. This results in 6 reflectional symmetries.
Overall, a regular hexagon has 6 lines of symmetry and 6 rotational symmetries.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3e2a46ee-88e3-4252-8f0b-8f51e15168b2%2F5839855a-fbcc-4873-b3f1-3dfd80deebfa%2Faoftkyu.jpeg&w=3840&q=75)
Transcribed Image Text:**Question 5**
How many symmetries (number of each type: line, rotation, etc.) does a regular hexagon have? Explain.
[Image of a regular hexagon]
**Explanation:**
A regular hexagon has a total of 12 symmetries. These symmetries include:
1. **Rotational Symmetries**:
- The hexagon can be rotated around its center at angles of 0°, 60°, 120°, 180°, 240°, and 300°. This gives us 6 rotational symmetries.
2. **Reflectional Symmetries**:
- The hexagon can be reflected along 6 different axes of symmetry: each passing through one vertex and the midpoint of the opposite side, or each passing through the midpoints of opposite sides. This results in 6 reflectional symmetries.
Overall, a regular hexagon has 6 lines of symmetry and 6 rotational symmetries.
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