4.G.3: Lines of Symmetry
Also written as 4.G.A.3 and CCSS.MATH.CONTENT.4.G.A.3 · Cluster: Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
The Official Wording
Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry.
Common Core State Standards, Grade 4, Geometry · Read it at the source · Checked October 14, 2026
What 4.G.3 Means in Plain English
Fourth graders fold a shape so its halves land exactly on each other: that fold is a line of symmetry. The letter H folds two ways, A one way, and N not at all, though it looks the same upside down. Then they draw each line with a ruler.
Halves were equal shares in 2nd and 3rd grade (2.G.3, 3.G.2), but equal halves are not always mirror halves. The fold returns in 8th grade as a reflection, a flip that keeps every length and angle the same (8.G.1), and as a move that proves two figures congruent (8.G.2).
4.G.3 I Can Statements
- I can test a line of symmetry by folding along it.
- I can draw every line of symmetry a shape has.
- I can finish a drawing so it matches across a line.
4.G.3 Worked Example
Three paper shapes folded every way a student might try, including the diagonal fold that fools most of the class.
Cut out a 4 by 6 rectangle, a square, and a parallelogram with slanted sides of two different lengths. Fold each one every way you can think of. How many lines of symmetry does each shape have?
- Fold the rectangle top edge to bottom edge. The halves match exactly.Rectangle: 1 line, across the middle
- Fold it left edge to right edge. The halves match again.Rectangle: 2 lines
- Fold it corner to corner. The two triangles are the same size, but their corners stick out past each other.Rectangle’s diagonal: not a line of symmetry
- The square passes all four folds, the diagonals too, because its four sides are the same length.Square: 4 lines
- The parallelogram fails every fold, even the diagonal that cuts it into two equal triangles.Parallelogram: 0 lines
Check it: Stand a small mirror on each line you drew. The shape and its reflection should rebuild the whole figure, and on the rectangle’s diagonal they do not.
Common Mistakes with 4.G.3
Equal halves taken for mirror halves
A rectangle’s diagonal drawn as a line of symmetry because it cuts the rectangle into two equal triangles
Try this: Cut out the rectangle and fold it along the diagonal. The corners stick out, so equal halves are not always matching halves.
Only checking up and down
The letter B given no line of symmetry because it does not fold left to right
Try this: Try every direction: up and down, side to side and both diagonals. Fold or hold a mirror on each one before deciding.
Finishing the picture by copying
Half a tree on grid paper finished by copying it beside the line, so both branches point the same way
Try this: Count grid squares from the line to each point, then mark the matching point the same number of squares away on the other side.
Where 4.G.3 Fits
Practice 4.G.3
Quick Check
- How many lines of symmetry does a square have?
- Does the capital letter S have a line of symmetry?
- How many lines of symmetry does a triangle with three equal sides have?