Concept 6 of 6
The Mirror Grid: Symmetry
Today's big idea
If a shape folds in half so both sides match, it has a line of symmetry.
A square has 4 lines. A heart has 1. A scribble has none.
How it works
👀 What's going on?
Fold a paper heart down the middle and the two halves land exactly on top of each other. That fold line has a name, and finding every line that works is the whole skill.
💡 Here's the trick
Look at the mirror line above. Everything on the left matches everything on the right, sitting the same distance out from the line. That is what a line of symmetry means. Fold along it and the halves land on each other, and a shape can have several such lines or none at all.
🪄 How to do it
- 1.Draw a possible fold line through the shape, like the one in the picture above.
- 2.Check whether both halves land exactly on each other, then try every other line you can find.
✍️ Try it
How many lines of symmetry does the capital letter H have? And what about the letter R?
H folds both across and down the middle, so it has 2 lines. R folds no way at all, so it has 0 lines. None is a perfectly good answer, and papers include such shapes deliberately.
⚠️ Watch out
You might be thinking any line splitting a shape into two equal halves is a line of symmetry. Equal size is not enough, because the halves have to be mirror images. A diagonal across a rectangle makes two equal triangles and is still not a line of symmetry.
🌟 Why this matters
Rangoli patterns, butterfly wings, the front of a car and most buildings are built on symmetry, because balance is what makes something look right.
Exam tip: Test the diagonals separately, because a square has them as lines of symmetry and a rectangle does not.
Watch me solve one
Quanta solves it
“Watch how I think through one of these — then you try.”
THE PROBLEM
Complete the right side across the mirror line:
- 1
The fold test
The pink line is the mirror. The right side must be the left side flipped, so the halves land on each other when folded.
- 2
Mirror one square
The square touching the line gets a twin touching it on the other side, the same distance out:
- 3
Mirror every square
Do that for all three, and the L flips into a backwards L:
- 4
Answer ✓
A backwards L — fold it and the halves match
Now you try one — same steps, different story 👇
See it in action
⚡ Time to play!
Select at least 4 cells on the LEFT/TOP half to unlock the question. The mirror side reflects automatically!
0 / 4 cells selected
Quick check
✅ VERIFICATION
How many lines of symmetry does a rectangle that is not a square have?
⚡ Finish the activity above first to answer.
Keep going!