Line Symmetry

Line symmetry, also known as reflection symmetry, occurs when a figure can be divided into two identical halves by a line. The line along which the figure is divided is called the line of symmetry. If a figure has more than one line of symmetry, it is said to have multiple lines of symmetry.

Properties of Line Symmetry

1. A figure with line symmetry reflects onto itself across the line of symmetry.
2. The line of symmetry divides the figure into two mirror-image halves.
3. If a figure has a line of symmetry, any point on one side of the line will have a corresponding point on the other side of the line that is equidistant from the line of symmetry.

Examples of Figures with Line Symmetry

Common examples of figures with line symmetry include:

• Equilateral triangle
• Rectangle
• Square
• Circle
• Pentagon
• Hexagon

Identifying Line Symmetry

To identify line symmetry in a figure, you can follow these steps:

1. Draw the figure on a piece of graph paper or use a drawing software.
2. Identify a possible line of symmetry in the figure (e.g., vertical, horizontal, or diagonal lines).
3. Check if the figure can be divided into two mirror-image halves along the identified line of symmetry.
4. If the figure can be divided in such a way, then it has line symmetry. If not, try another line of symmetry until all possibilities are exhausted.

Study Guide for Line Symmetry

To study line symmetry, it is important to understand the following concepts:

1. Definition of line symmetry and line of symmetry.
2. Properties of figures with line symmetry.
3. Identifying line symmetry in various geometric figures.
4. Drawing figures with line symmetry and identifying the lines of symmetry.
5. Practice problems involving line symmetry.

Understanding line symmetry is important in geometry and can be applied to various real-world objects and designs. It is a fundamental concept that lays the groundwork for more advanced topics in mathematics and art.