Point Symmetry

Point symmetry, also known as central symmetry, occurs when a figure can be rotated 180 degrees around a central point and still look the same. The central point is called the center of symmetry.

Properties of Point Symmetry:

1. A figure has point symmetry if it looks the same after a 180-degree rotation around a central point.
2. The center of symmetry is the point around which the figure is rotated.
3. Every point of the figure has a corresponding point on the opposite side of the center of symmetry, at the same distance from the center.
4. Figures with point symmetry include regular polygons, circles, and some letters and symbols.

Identifying Point Symmetry:

To determine if a figure has point symmetry, you can follow these steps:

1. Identify a central point around which the figure could be rotated.
2. Rotate the figure 180 degrees around the central point.
3. Check if the figure looks the same after the rotation. If it does, the figure has point symmetry.

Examples of Figures with Point Symmetry:

Here are some examples of figures with point symmetry:

• Regular Hexagon: A hexagon has point symmetry if it looks the same after a 180-degree rotation around its center.
• Circle: A circle has point symmetry with its center being the central point of symmetry.

Study Guide:

To study point symmetry, make sure to:

• Understand the concept of central symmetry and how it applies to different figures.
• Practice identifying the central point of symmetry in various figures.
• Work on rotating figures around the central point to determine if they have point symmetry.

Remember that point symmetry is an important concept in geometry and can be found in various shapes and objects around us.