Symmetry and Lines of Symmetry
Grade 4 · Math · Study Guide
Learn what symmetry means and how to find lines of symmetry in shapes and real-world objects.
A shape has symmetry when it can be folded or reflected so that both halves match exactly. The fold line is called the line of symmetry. When you fold along this line, both sides land perfectly on top of each other — like a mirror image.
Some shapes have just one line of symmetry. An isosceles triangle has exactly one: the line that goes straight down the middle from the top vertex to the base. Other shapes have many lines of symmetry. A square has 4 lines of symmetry: two going through opposite corners (diagonal) and two going through the midpoints of opposite sides.
A circle is the most symmetrical shape of all — it has an infinite number of lines of symmetry! Any diameter of a circle is a line of symmetry.
Symmetry appears everywhere in nature and art. Butterflies, snowflakes, leaves, and faces all show symmetry. Many letters of the alphabet also have lines of symmetry: A, M, T, U, V, and W have a vertical line of symmetry. B, C, D, E, and K have a horizontal one.
Key terms
- Symmetry
- A shape has symmetry when one half mirrors the other exactly.
- Line of symmetry
- The line along which a shape can be folded so both halves match perfectly.
- Reflection
- A mirror image of a shape across a line of symmetry.
Flashcards
- Line of symmetry
- A line that divides a shape into two mirror-image halves.
- Lines of symmetry in a square
- 4 — two through midpoints of sides, two through corners (diagonals).
- Lines of symmetry in a rectangle (non-square)
- 2 — through the midpoints of opposite sides only.
- Lines of symmetry in a circle
- Infinite — any diameter works as a line of symmetry.
- Isosceles triangle lines of symmetry
- 1 — through the vertex angle to the midpoint of the base.
- Does the letter A have symmetry?
- Yes — vertical line of symmetry down the center.
Practice questions
How many lines of symmetry does a square have?
- 1
- 2
- 4
- 8
Show answer
Answer: 4
A square has 4 lines of symmetry: 2 through the midpoints of opposite sides, and 2 through opposite corners.
A circle has exactly 2 lines of symmetry.
Show answer
Answer: False
A circle has infinitely many lines of symmetry. Any line through the center (any diameter) is a line of symmetry.
The line that divides a shape into two matching mirror-image halves is called the line of ___.
Show answer
Answer: symmetry
The fold line that creates two perfectly matching halves is called the line of symmetry.
Which letter has a vertical line of symmetry?
- B
- P
- A
- L
Show answer
Answer: A
The letter A has a vertical line of symmetry down its center. B has a horizontal line of symmetry; P and L have none.
A rectangle that is not a square has ___ lines of symmetry.
Show answer
Answer: 2
A non-square rectangle has 2 lines of symmetry: one horizontal and one vertical through the midpoints. Its diagonals are NOT lines of symmetry.
Fun facts
- A snowflake always has 6 lines of symmetry — and no two snowflakes are exactly alike, yet they all follow the same symmetry pattern!
- The human face is nearly (but not perfectly) symmetric — if you photograph just the left or right half and mirror it, the result looks slightly different from the real face.
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