Shapes in the Plane
Primary 4 · Mathematics
Shapes in the Plane
Lesson 5 of 5
25 min
Let's begin
Ishimwe's grandmother paints imigongo, the famous patterned art from eastern Rwanda. "Look," she says, folding a paper copy of her pattern down the middle. "The left side lands exactly on the right side."
When a shape folds into two matching halves, the fold line is a line of symmetry.
A line of symmetry cuts a shape into two halves that match exactly, like a mirror image. If you fold along the line, one half covers the other with nothing sticking out.
| Shape | Lines of symmetry |
|---|---|
| Square | 4 |
| Equilateral triangle | 3 |
| Rectangle | 2 |
| Rhombus | 2 (its diagonals) |
| Isosceles triangle | 1 |
| Kite | 1 |
| Parallelogram | 0 |
| Scalene triangle | 0 |
The diagonal of a rectangle is not a line of symmetry. Fold a rectangle of paper corner to corner and look: the two halves do not sit on top of each other. Only the two folds through the middles of the sides work.
Cut the shape out of paper. Fold it. If the two halves match exactly, the fold is a line of symmetry. Try every way you can think of, then count.
Tip
Fold and check. A line of symmetry is a perfect fold: the two halves match like your left hand and your right hand.
Work each one in your exercise book first. Then tap Show answer to check.
How many lines of symmetry does a square have?
Answer: 4: two through the middles of the sides and two along the diagonals.
How many lines of symmetry does a kite have?
Answer: 1: the fold from the top point down to the bottom point.
Does a scalene triangle have a line of symmetry?
Answer: No. Its sides are all different, so no fold makes matching halves.
Uwase folds a rectangle from corner to corner. Is that a line of symmetry?
Answer: No. The halves do not match. A rectangle has only 2 lines of symmetry, through the middles of its sides.
Which capital letters have a vertical line of symmetry: A, F, M, R?
Answer: A and M.
What you learned today
Sources and credits
The imigongo-style pattern is a simple drawing made by Ganzaa, not a copy of any artist's work. The stories, Rwandan examples, diagrams and practice questions were written by Ganzaa.
Quick check
Match each shape to its number of lines of symmetry.
Tap one on the left, then its partner on the right.
