Linear symmetry, also known as line symmetry or mirror symmetry, describes a specific type of symmetry where a shape or pattern looks the same on both sides of a dividing line. According to the reference, "when we draw a line segment exactly in the middle of a pattern or drawing, if one part is identical to the other then the pattern is said to be linearly symmetrical."
Understanding Linear Symmetry
- The Line of Symmetry: The imaginary line that divides the shape or pattern. It acts like a mirror.
- Identical Halves: The two halves created by the line of symmetry are mirror images of each other. They are congruent (identical in shape and size).
Characteristics of Linearly Symmetrical Shapes:
- If you were to fold the shape along the line of symmetry, the two halves would perfectly overlap.
- Each point on one side of the line of symmetry has a corresponding point on the other side, equidistant from the line.
Examples of Linear Symmetry:
Many things in the real world exhibit linear symmetry:
- Letters: The letters A, H, I, M, O, T, U, V, W, X, and Y (in uppercase) all possess vertical line symmetry.
- Shapes: Squares, rectangles, circles, and isosceles triangles all have one or more lines of symmetry.
- Objects: Butterflies, faces (approximately), and many buildings often display linear symmetry.
Identifying Linear Symmetry:
- Visualize or draw a line: Try to imagine or draw a line through the shape or pattern.
- Check for mirror images: Does the line create two halves that are mirror images of each other?
- Folding test: Mentally "fold" the shape along the line. Would the two halves match up perfectly?
If the answer to both questions is yes, then the shape or pattern possesses linear symmetry.
