What Is a Line of Symmetry? Fun Examples & Easy Guide for Kids

Have you ever folded a piece of paper, cut out a heart, and opened it to find two identical halves? Or stared at a ladybug and noticed its spots matched perfectly on both sides? That’s the magic of a line of symmetry. A hidden “mirror line” that makes things look balanced and equal.

Symmetry isn’t just pretty; it’s everywhere! From the stars in the sky to the cookies your mom bakes, understanding symmetry helps kids notice patterns in math and the world. At WuKong Education, we turn this cool concept into easy, playful lessons—let’s dive in and uncover what a line of symmetry really is!

What Is a Line of Symmetry? Simple Definition for Kids

Let’s start with the basics: A line of symmetry (also called a “line of reflection”) is an imaginary straight line that divides a shape or object into two exactly identical halves. If you fold the shape along this line, one half will fit perfectly over the other—like two puzzle pieces that match!

Here’s the math part (made simple!): The two halves are called “mirror images” of each other. That means every point on one side of the line has a matching point on the other side, at the same distance from the line.

Definition

Let’s introduce the concept of line symmetry first: If points A and B are on opposite sides of a line and are the perpendicular bisectors of line segment AB, then points A and B are said to be symmetrical to each other with respect to the line, and points A and B are called symmetrical points with respect to the line. The line is called the axis of symmetry.

Definition 1

On a plane, if all the points of figure F are symmetrical with respect to a line on the plane, then the line is called the axis of symmetry of the figure.

Definition 2

On a plane, if there is a line such that the set of all symmetrical points of figure F with respect to this line is still the figure itself, then the figure is called an axisymmetric figure, and the line is its axis of symmetry.

The three figures in the picture below have two, one and four axes of symmetry respectively.

What Is a Line of Symmetry? Theorem

① The distance between any point on the axis of symmetry and its corresponding symmetrical point is equal.
② The line segment connecting the symmetrical points is perpendicular to the axis of symmetry.
Corollary: If two figures are symmetrical about a certain line axis, then these two figures are congruent.

Common Symmetrical Figures

Several common symmetrical figures and central symmetrical figures

• Symmetrical figures: line segments, angles, isosceles triangles, equilateral triangles, rhombuses, rectangles, squares, isosceles trapezoids, circles, hyperbolas (with two axes of symmetry), ellipses (with two axes of symmetry), parabolas (with one axis of symmetry), etc.
• Number of axes of symmetry: an angle has one axis of symmetry, which is the line of the angle’s bisector; an isosceles triangle has one axis of symmetry, which is the perpendicular bisector of the base; an equilateral triangle has three axes of symmetry, which are the perpendicular bisectors of the three sides; a rhombus has two axes of symmetry, which are the lines of the two diagonals; a rectangle has two axes of symmetry, which are the lines connecting the midpoints of the two pairs of opposite sides;
• Central symmetrical figures: line segments, parallelograms, rhombuses, rectangles, squares, circles, etc.
• Symmetry center: the symmetry center of a line segment is the midpoint of the line segment; the symmetry center of a parallelogram, rhombus, rectangle, or square is the intersection point of the diagonals; the symmetry center of a circle is the center of the circle.
• Explanation: Line segments, rhombuses, rectangles, squares, and circles are both symmetrical figures and central symmetrical figures.

Symmetry transformations in the coordinate system and central symmetry transformations

Point P(x, y) is symmetric to point P₁ about the x-axis, and its coordinates are (x, -y); point P₂ is symmetric to it about the y-axis, and its coordinates are (-x, y). The coordinates of point P3, which is symmetric to the origin, are (-x, -y). This rule can also be remembered as: for points symmetric about the y-axis (x-axis), the y-coordinates (x-coordinates) are the same, and the x-coordinates (y-coordinates) are opposite numbers. For points symmetric about the origin in a central symmetry, the x-coordinate is the opposite of the original x-coordinate, and the y-coordinate is the opposite of the original y-coordinate, that is, both the x-coordinate and y-coordinate are multiplied by -1.

Line of Symmetry Examples: Shapes & Real Objects

Look around your home, you’ll find symmetry everywhere:

• A pair of scissors (fold along the center, and both blades match)
• A dinner plate (any line through the middle is a line of symmetry)
• A snowflake (6 perfect lines of symmetry—nature’s math art!)
• A book (vertical line down the spine makes two matching halves)

Fun Interactive Activities to Practice Symmetry

Learning is better with play! Try these easy activities with your kid.

1. Symmetry Scavenger Hunt: Grab a pencil and paper. Find 5 objects at home with lines of symmetry (e.g., cup, clock, t-shirt). Draw each object and mark its symmetry line.
2. Mirror Art: Place a mirror vertically on a piece of paper. Draw half a flower or animal next to the mirror—see the full symmetric shape!
3. Fold & Cut: Fold construction paper in half. Cut out a random shape (e.g., star, fish) and unfold—you’ve made a symmetric design!

Pro tip: Turn it into a game! For every symmetric object your kid finds, could you give them a sticker? Celebrate their wins—math should feel fun!

FAQs About Line of Symmetry

Let’s Find Symmetry Together!

To wrap up: A line of symmetry is a line that splits a shape into two identical mirror halves. It comes in vertical, horizontal, and diagonal types—and you can find it in butterflies, squares, even your favorite toy!

Want to turn symmetry into a superpower? Join WuKong Math free trial lesson! Our teachers make math fun and easy, so your kid will master symmetry and more in no time. 

Delvair | WuKong Math Teacher

Delvair holds a degree in Physics from the Federal University of Maranhão, Brazil. With over six years of experience, she specializes in teaching mathematics, with a particular emphasis on Math Kangaroo competitions. She firmly believes that education is the cornerstone of society’s future. Additionally, she holds the conviction that every child can learn given the right environment and guidance. In her spare time, she enjoys singing and tending to her plants.