Symmetry: slide, flip and turn
Find lines of symmetry, complete a mirror picture and learn the three moves: slide, flip and turn. Then rotational symmetry and enlargement. Read one step, play with it, then tap “I understand this”.
Lines of symmetry
A shape is symmetrical if you can fold it on a line so that the two halves fit exactly on top of each other. That line is a line of symmetry.
The fold test
Choose a shape. Guess how many lines of symmetry it has, then tap the button.
Test it with paper: cut out the shape and fold it. Do the edges match exactly? Then you have found a line of symmetry.
Every point on a circle is the same distance from the centre. Whatever line you draw through the middle, the two halves are exactly the same. That is why there are endlessly many.
Complete the mirror picture
In a mirror picture (reflection) every point is just as far from the mirror line as its partner, only on the other side. Count the squares from the line.
The mirror grid
Tap the squares on the other side of the red line to make the mirror image. Then tap “Check”.
A square that is 1 square from the line has a mirror image that is also just 1 square from the line. Do not count from the edge of the grid.
A mirror shows everything as far behind the glass as it is in front of it. If you stand 1 m in front of a mirror, your image seems to stand 1 m behind the glass. That is why we count from the mirror line, not from the edge.
Three moves: slide, flip and turn
A transformation moves a shape. In all three of these moves the shape stays the same size and keeps its shape:
- Slide (translation): the shape glides to a new place and still points the same way.
- Flip (reflection): the shape is turned back to front, like in a mirror.
- Turn (rotation): the shape turns about a point, like the hands of a clock.
The movement lab
Tap the buttons and watch how the shape moves.
Slide, flip and turn only move the shape; they do not stretch or squash it. Every side stays the same length and every angle stays the same size. The new shape is congruent to the old one: exactly the same shape and size.
Which move was it?
Move detective
Look at how shape A got to B. Is it a slide, a flip or a turn?
Correct: 0
Ask two questions. Does B point the same way as A? Then it is a slide. Is B back to front (left and right swapped)? Then it is a flip. Otherwise it is a turn.
Rotational symmetry
A shape has rotational symmetry if it fits into its own outline before you have turned it a full turn (360°). The order is how many times it fits in one full turn.
Turn and look
Choose a shape and turn it 30° at a time about the red dot.
A windmill wheel has no line of symmetry, but it does have rotational symmetry of order 4. The two kinds of symmetry are not the same.
After a full turn of 360° every shape fits again, even a heart. That is why a shape only counts as rotationally symmetrical if it fits before 360°.
Enlarge and reduce
In an enlargement or reduction every side is multiplied by the same number: the scale factor. The shape stays the same shape (the angles do not change), but the size changes.
The scale machine
Choose a scale factor and compare A and B.
If every side is multiplied by the same number, the ratio between the sides does not change. A square that is enlarged stays a square with right angles. Only the size changes, not the shape.
Check yourself
- A line of symmetry folds a shape into two halves that match exactly.
- Mirror image: every point as far from the line, on the other side.
- Slide = translation, flip = reflection, turn = rotation. The size stays the same.
- Order of rotational symmetry = how many times it fits in one full turn.
- Scale factor: every side × the same number. The angles stay the same.
Write these points in your maths book. Read them again the night before the test.
Quick questions
Tap an answer. If you get one wrong, read why and go back to that step. You get new questions every time.
You ticked all 6 steps! Now you are ready for the quiz.- Practice sheet for this classQuestions + memo · 2 A4 pagesPractice sheet
- Space and shape8 pages · PDFPaperMemo
- Geometry8 pages · PDFPaperMemo
Ready for more? The Grade 6 symmetry quiz gives you new questions every time.
- One step a day is enough. Ten calm minutes work better than an hour the night before the test.
- Look for symmetry together at home and outside: a leaf, a butterfly, letters on a sign. Ask: “Where would you fold it?”
- Ask your child to tell you the rule in their own words. If they can explain it, they understand it.
- The ticks (“I understand this”) are saved on this device only. We never ask for names or emails.
Follows CAPS for Grade 6 Maths. Always check your teacher’s notes and textbook too.