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4. Draw all the lines of symmetry. Locate the center of rotational symmetry.

4. Draw all the lines of symmetry. Locate the center of rotational symmetry.

Elementary Geometry For College Students, 7e
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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This is a geometry question.
### Symmetry Educational Exercise #### Questions: 1. **Draw all the lines of symmetry. Locate the center of rotational symmetry.** 2. **Draw all symmetries explicitly.** a. What kinds are there? b. How many are rotations? (Include 360° rotational symmetry, i.e., the identity symmetry) c. How many are reflections? #### Diagram: <div align="center"> <span style="font-weight: bold;"> A B D <span style="display: inline-block; width: 200px; height: 200px; border: 1px solid black;"></span> B </span> <span style="display: inline-block; margin-top: -50px;"> C </span> </div> --- #### Explanation: - **Lines of Symmetry**: - A line of symmetry divides a shape into two identical halves that are mirror images of each other. In the given diagram of a square ABCD: - There are two lines of symmetry running through the midpoints of opposite sides (horizontal and vertical). - There are also two diagonal lines of symmetry that run from one vertex to the opposite vertex. - **Rotational Symmetry**: - A shape has rotational symmetry if it can be rotated (less than a full circle) about a center point and still looks the same as it did before the rotation. For a square: - The center of rotational symmetry is the center of the square. - There are four rotations that map the square onto itself: 0° (identity transformation), 90°, 180°, and 270°. - **Reflection Symmetry**: - An object has reflection symmetry if there is a line through it such that one half is a mirror image of the other half. - The square ABCD has four lines of reflection symmetry: one vertical through the midpoints of A and C, one horizontal through the midpoints of B and D, and two diagonals through the vertices. By identifying these symmetries, students can better understand geometric properties and transformations.
Transcribed Image Text:### Symmetry Educational Exercise #### Questions: 1. **Draw all the lines of symmetry. Locate the center of rotational symmetry.** 2. **Draw all symmetries explicitly.** a. What kinds are there? b. How many are rotations? (Include 360° rotational symmetry, i.e., the identity symmetry) c. How many are reflections? #### Diagram: <div align="center"> <span style="font-weight: bold;"> A B D <span style="display: inline-block; width: 200px; height: 200px; border: 1px solid black;"></span> B </span> <span style="display: inline-block; margin-top: -50px;"> C </span> </div> --- #### Explanation: - **Lines of Symmetry**: - A line of symmetry divides a shape into two identical halves that are mirror images of each other. In the given diagram of a square ABCD: - There are two lines of symmetry running through the midpoints of opposite sides (horizontal and vertical). - There are also two diagonal lines of symmetry that run from one vertex to the opposite vertex. - **Rotational Symmetry**: - A shape has rotational symmetry if it can be rotated (less than a full circle) about a center point and still looks the same as it did before the rotation. For a square: - The center of rotational symmetry is the center of the square. - There are four rotations that map the square onto itself: 0° (identity transformation), 90°, 180°, and 270°. - **Reflection Symmetry**: - An object has reflection symmetry if there is a line through it such that one half is a mirror image of the other half. - The square ABCD has four lines of reflection symmetry: one vertical through the midpoints of A and C, one horizontal through the midpoints of B and D, and two diagonals through the vertices. By identifying these symmetries, students can better understand geometric properties and transformations.
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