4th Grade Lines of Symmetry Lesson (Free PDF)
This grade 4 symmetry lesson for 4th Grade covers lines of symmetry (Common Core 4.G.A.3), with a free PDF to print.
A figure has line symmetry when you can fold it along a line so the two halves match exactly. That fold line is called a line of symmetry. A square has 4 lines of symmetry, a rectangle that is not a square has 2, and a slanted parallelogram has none. Many letters and animals are symmetric too.
Grade 4 · Common Core State Standards: 4.G.A.3
Key facts in this grade 4 symmetry lesson
- A line of symmetry splits a figure into two matching halves.
- A square has 4 lines of symmetry, a rectangle has 2, and an equilateral triangle has 3.
- A regular polygon with n sides has n lines of symmetry.
- Some figures, like a slanted parallelogram, have no lines of symmetry.
- Check by folding: the edges and corners must line up exactly.
What is a line of symmetry?
Fold a piece of paper with a heart cut out of it. If the two halves of the heart land exactly on top of each other, the fold is a line of symmetry. A figure with at least one such line is line-symmetric. Look at the heart and the butterfly: the dashed line cuts each one into two mirror images.
| Heart | Butterfly |
|---|---|
|
|
|
A figure is line-symmetric if it can be folded along a line into two parts that match exactly. The fold line is its line of symmetry. A figure can have one line, several lines, or none.
How many lines of symmetry do shapes have?
Count the fold lines that make the halves match. A square can be folded in half across, up and down, or along either diagonal, so it has 4 lines. A rectangle that is not a square has only 2, because its diagonals do not work.
| Square | Rectangle | Equilateral triangle |
|---|---|---|
| 4 lines | 2 lines | 3 lines |
| Fold up, across, and along each diagonal. | Fold up and across only. | One fold from each corner. |
Do letters and everyday things have symmetry?
Yes. The letters A, H, M, T, and X can be cut by a vertical line into matching halves. The letters B, E, and H can be cut by a horizontal line. The letters F, L, and S have no line of symmetry.
Example. How many lines of symmetry does a regular pentagon have?
- A regular pentagon has 5 equal sides and 5 equal angles.
- Each fold runs from a corner to the middle of the opposite side.
- There are 5 corners, so there are 5 lines of symmetry.
Grade 4 symmetry lesson: questions and answers
What is a line of symmetry?
A line of symmetry is a fold line that cuts a figure into two halves that match exactly, like a mirror image. If the halves do not match, the line is not a line of symmetry.
How many lines of symmetry does a rectangle have?
A rectangle that is not a square has 2 lines of symmetry: one up and down, and one across. The diagonals are not lines of symmetry for a rectangle.
Can a shape have no lines of symmetry?
Yes. A slanted parallelogram and a triangle with three different side lengths have no lines of symmetry. No fold makes the two halves match.
How many lines of symmetry does a regular polygon have?
A regular polygon has as many lines of symmetry as it has sides. A regular pentagon has 5, a regular hexagon has 6, and a regular octagon has 8.
Which letters have a vertical line of symmetry?
The capital letters A, H, M, T, U, V, W, X, and Y have a vertical line of symmetry. The letters F, G, J, L, P, R, and S have none.
How to use this grade 4 symmetry lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the grade 4 symmetry lesson as a PDF with the button below and keep it with your notes.
All Grade 4 chapters: Grade 4 math.
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