Worked examples
The question
Question: how many lines of symmetry does an equilateral triangle have?
1 Try the folds
Imagine folding the shape along a line.
If the two halves match exactly, it is a line of symmetry.
Fold through a corner and the middle of the opposite side.
The halves match: line 1.
Fold through a corner and the middle of the opposite side.
The halves match: line 2.
Fold through a corner and the middle of the opposite side.
The halves match: line 3.
2 Count the lines
We found 3.
So an equilateral triangle has 3 lines of symmetry.
lines of symmetry = 3
Careful!
Each fold goes through a corner and the middle of a side.
Count each fold once: 3, not 6.
Careful: not 6 ✗
3 Check
Let's check: a regular shape has as many lines of symmetry as sides.
3 sides, 3 lines.
Right!
3 sides → 3 lines
Let's look back.
First: try the folds.
Then: count the lines.
Last: check.
Answer lines of symmetry = 3
▶ Watch it solved
The question
Question: how many lines of symmetry does a rectangle have?
1 Try the folds
Imagine folding the shape along a line.
If the two halves match exactly, it is a line of symmetry.
Fold straight down the middle.
The halves match: line 1.
Fold across the middle.
The halves match: line 2.
Fold along a diagonal.
The corners do not meet.
It is not a line of symmetry.
2 Count the lines
We found 2.
So a rectangle has 2 lines of symmetry.
lines of symmetry = 2
Careful!
A rectangle has 2, not 4.
Its diagonals are not lines of symmetry: the corners do not meet.
Careful: not 4 ✗
3 Check
Let's check.
Fold along line 1: this corner lands on that corner.
Across this line too, each corner lands on a corner.
Every corner lands on a corner.
Right!
every corner lands on a corner
Let's look back.
First: try the folds.
Then: count the lines.
Last: check.
Answer lines of symmetry = 2
▶ Watch it solved
The question
Question: how many lines of symmetry does a parallelogram have?
1 Try the folds
Imagine folding the shape along a line.
If the two halves match exactly, it is a line of symmetry.
Fold straight down the middle.
The corners do not meet.
It is not a line of symmetry.
Fold across the middle.
The corners do not meet.
It is not a line of symmetry.
Fold along a diagonal.
The corners do not meet.
It is not a line of symmetry.
2 Count the lines
No fold works.
So a parallelogram has 0 lines of symmetry.
lines of symmetry = 0
Careful!
A parallelogram leans.
Folding it down the middle or across the middle does not work.
Careful: not 2 ✗
Let's look back.
First: try the folds.
Last: count the lines.
Answer lines of symmetry = 0
▶ Watch it solved
