2-D shapes (age 8+)
Identify lines of symmetry in 2-D shapes presented in different orientations; recognise line-symmetric figures and draw lines of symmetry
What a learner can do afterwards
- Find all lines of symmetry in a rectangle, square, and equilateral triangle
- Determine whether a given shape has a line of symmetry when rotated
- Identify which shapes in a set have exactly one line of symmetry
- Determine how many lines of symmetry a regular hexagon has
- Draw all lines of symmetry for a given figure
- Identify which figures from a set are not line-symmetric
The lesson
A line of symmetry is a fold line. Fold a shape exactly on that line, and both halves land right on top of each other and match perfectly. You already flipped shapes on a grid before. A line of symmetry is the exact spot to flip along so the shape ends up looking exactly like it did before the flip.
A rectangle that is not a square has only 2 lines of symmetry, straight through the middles of its sides. Its corner-to-corner lines do not match, so they don't count. An equilateral triangle, with all three sides the same length, has 3 lines of symmetry, one running from each corner to the middle of the opposite side.
Turning a shape does not change how many lines of symmetry it has. Stand a square up on one corner so it looks like a diamond. It still has 4 lines of symmetry. Two of them just look diagonal now instead of straight up and down.
To find every line of symmetry, imagine folding the shape in as many directions as you can: up-down, side-to-side, and both diagonals. Keep only the folds where both halves match exactly.
A line of symmetry is a fold line where both halves match exactly, and turning the shape never changes how many it has.
Watch it
Where it sits
Learn first
This opens up
Where this leads
Jobs that lean on this skill. Follow one to see everything it is built on.
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.