What is Line Symmetry? Definition and Examples in High School Geometry

📚 Quick Study Guide

• 🔍 Definition: A figure has line symmetry if it can be folded along a line so that the two halves match exactly. This line is called the line of symmetry.
• 📐 Identifying Symmetry: Look for a line that divides the figure into two congruent halves that are mirror images of each other.
• ✨ Examples: Common examples include circles, squares, rectangles, some triangles, and many letters of the alphabet (A, H, I, M, O, T, U, V, W, X, Y).
• 🧮 Mathematical Representation: If a point $(x, y)$ is on a figure, and the figure has line symmetry about the y-axis, then the point $(-x, y)$ is also on the figure. Similarly, if the figure has line symmetry about the x-axis, the point $(x, -y)$ is also on the figure.
• 💡 Tips: Visualize folding the shape along the potential line of symmetry. If the two halves overlap perfectly, it's a line of symmetry.
• ✍️ Non-Examples: Figures that do not have matching halves when folded do not possess line symmetry. Irregular shapes often lack line symmetry.

🧪 Practice Quiz

1. Which of the following letters has a vertical line of symmetry?
   1. B
   2. C
   3. A
   4. J
2. Which shape does NOT have any lines of symmetry?
   1. Circle
   2. Square
   3. Parallelogram
   4. Isosceles Triangle
3. A rectangle has how many lines of symmetry?
   1. 0
   2. 1
   3. 2
   4. 4
4. Which of the following has an infinite number of lines of symmetry?
   1. Square
   2. Circle
   3. Equilateral Triangle
   4. Rectangle
5. If a point (3, 5) lies on a figure with line symmetry about the y-axis, which other point must also lie on the figure?
   1. (3, -5)
   2. (-3, 5)
   3. (-3, -5)
   4. (5, 3)
6. Which of the following road signs most likely exhibits line symmetry?
   1. A rectangular speed limit sign
   2. A circular yield sign
   3. A triangular warning sign
   4. A diamond-shaped warning sign
7. An isosceles trapezoid has how many lines of symmetry?
   1. 0
   2. 1
   3. 2
   4. 4