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: A B D B C ---#### 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.

NOTE : Sorry buddy as per our guidelines we should answer only first question if multiple questions…

Answered: 4. Draw all the lines of symmetry.…

Math

Geometry

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

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.

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