Problem Description:
The image provided explains the concept of
rotational symmetry for 2D shapes. Rotational symmetry is defined as the property of a shape that allows it to fit into itself when rotated around a central point. The number of times the shape fits into itself during a full rotation (360°) is called the
order of rotational symmetry.
The task appears to be to understand and identify the order of rotational symmetry for various 2D shapes shown in the image.
---
Solution Explanation:
#### Key Concepts:
1.
Rotational Symmetry: A shape has rotational symmetry if it looks the same after being rotated by a certain angle around its center.
2.
Order of Rotational Symmetry: The number of positions in which the shape looks identical during a full rotation (360°).
#### Steps to Determine the Order of Rotational Symmetry:
-
Identify the Central Point: All rotations are performed around the center of the shape.
-
Rotate the Shape: Rotate the shape in increments until it returns to its original position.
-
Count the Positions: Count how many times the shape looks identical during one full rotation (360°).
#### Analysis of Each Shape:
1.
Rhombus:
- A rhombus has rotational symmetry because it looks the same after a 180° rotation.
- It does not look the same after a 90° rotation.
-
Order of rotational symmetry: 2.
2.
Trapezium:
- A general trapezium does not have rotational symmetry because it does not look the same at any rotation other than 360°.
-
Order of rotational symmetry: 1 (or none, as stated in the image).
3.
Pentagon:
- A regular pentagon looks the same after rotations of 72°, 144°, 216°, 288°, and 360°.
-
Order of rotational symmetry: 5.
4.
Hexagon:
- A regular hexagon looks the same after rotations of 60°, 120°, 180°, 240°, 300°, and 360°.
-
Order of rotational symmetry: 6.
5.
Heptagon:
- A regular heptagon looks the same after rotations of approximately 51.43°, 102.86°, 154.29°, 205.71°, 257.14°, 308.57°, and 360°.
-
Order of rotational symmetry: 7.
6.
Octagon:
- A regular octagon looks the same after rotations of 45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°.
-
Order of rotational symmetry: 8.
7.
Star (5-pointed):
- A regular 5-pointed star looks the same after rotations of 72°, 144°, 216°, 288°, and 360°.
-
Order of rotational symmetry: 5.
8.
Heart:
- A heart shape does not have rotational symmetry because it does not look the same at any rotation other than 360°.
-
Order of rotational symmetry: 1 (or none, as stated in the image).
---
Final Answer:
The orders of rotational symmetry for the given shapes are summarized as follows:
- Rhombus:
2
- Trapezium:
None
- Pentagon:
5
- Hexagon:
6
- Heptagon:
7
- Octagon:
8
- Star:
5
- Heart:
None
$$
\boxed{2, \text{None}, 5, 6, 7, 8, 5, \text{None}}
$$
Parent Tip: Review the logic above to help your child master the concept of printable shapes for rotational symmetry.
