https://file.aiquickdraw.com/mathbot/file/1727940403193hejd6ayv.jpg

Let's analyze the symmetry properties of the three shapes in the image. Here’s how we can approach each:

### 1. **First shape (Peace symbol)**
- **Type of symmetry**: This shape has both rotational and reflectional (line) symmetry.
- **Number of lines of symmetry**: There are **3 lines of symmetry**. These lines divide the figure into identical halves.
- **Angles of rotation**: Since it has rotational symmetry, it can rotate by angles that are multiples of **120°** and look the same (i.e., 120°, 240°, and 360°).

### 2. **Second shape (Star-like pentagon)**
- **Type of symmetry**: This shape appears to have rotational symmetry but no reflectional symmetry.
- **Number of lines of symmetry**: **0 lines of symmetry**, because no line will divide it into mirror-image halves.
- **Angles of rotation**: Since it has rotational symmetry, it can rotate by angles that are multiples of **72°** (i.e., 72°, 144°, 216°, 288°, and 360°).

### 3. **Third shape (Parallelogram)**
- **Type of symmetry**: This shape only has rotational symmetry.
- **Number of lines of symmetry**: **0 lines of symmetry**, as no line divides the shape into identical halves.
- **Angles of rotation**: It has rotational symmetry of **180°**, meaning it can be rotated half a turn (180°) and still look the same.

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If you have more questions or need further clarification, feel free to ask!

Here are some related questions for further exploration:
1. What are some examples of objects in nature that show similar symmetry patterns?
2. Can you think of any shapes that have both reflectional and rotational symmetry, besides the peace symbol?
3. What is the significance of symmetry in design and architecture?
4. How does the order of rotational symmetry relate to the shape's internal angles?
5. Could a parallelogram have any other type of symmetry if modified?

**Tip**: Always check both line and rotational symmetry separately when analyzing shapes!

Investigate Symmetry for three shapes: a peace symbol, a star-like pentagon, and a parallelogram. Determine the types of symmetry, the number of lines of symmetry, and angles of rotation for each shape.

Explore the symmetry properties of three shapes: a peace symbol, a star-like pentagon, and a parallelogram. Learn how to identify lines of symmetry, rotational symmetry, and understand angles of rotation for each shape. Suitable for students in Grades 6-8.

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