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Non-Verbal Reasoning · Spatial transformations
NVR: rotation, reflection and symmetry
A free preview from the Athena Learning Library — the same lesson registered students learn from.
In this lesson: Recognise rotated and reflected shapes and count lines of symmetry.
Before you start
Turn a door handle: the handle moves, but it is still the same handle. Turning and flipping a shape work the same way — the shape never changes, only where it points and which way it leans.
Watch it happen
Watch a shape turn
Before the turn. Choose one corner of the hook shape and keep your eyes on it — it is about to travel.
A reflection is a flip, not a turn
A reflection flips the shape over the mirror line: left and right swap places, but top stays top. The flipped shape can never be matched by turning the original — that is how you tell a reflection from a rotation in a test.
Lines of symmetry
A regular pentagon has 5 lines of symmetry — one through each point and the middle of the opposite side. Fold along any dashed line and the two halves match exactly.
Your turn: match the target
Use the buttons to turn and flip the staircase shape until it matches the target exactly.
Your target:
The idea
A rotation turns a shape around its centre. The shape itself does not change: its size, shading and the order of its parts stay the same. Only its direction changes. A quarter turn is 90 degrees, a half turn is 180 degrees, and clockwise means the way clock hands move.
Use markers to check. Pick one easy feature, such as a dot at a tip, and follow just that feature around. After a 90-degree clockwise turn, a feature at the top moves to the right. After 180 degrees it is at the bottom. After 270 degrees clockwise it is on the left. Then check a second feature to make sure the whole shape has turned together.
A reflection is different: it flips the shape, as in a mirror, so left and right swap and the order of features reverses. A turned copy can match a rotation, but a flipped copy cannot. For symmetry, imagine folding the shape so the two halves match exactly; each fold line that works is one line of symmetry.
Worked example
The kite in the picture is turned 90° clockwise. Describe what the finished picture looks like, and say how you know it is a turn and not a reflection.
- Pick one corner of the kite and keep your eyes on it. A turn moves every point of the shape by the same angle around the centre — nothing stretches, nothing flips.
- Half-way (45° clockwise) the kite leans diagonally. It is still exactly the same kite, just pointing a new way.
- The turn finishes at 90° clockwise: a quarter turn. Compare start and finish — same size, same shape, right-hand side still the right-hand side. A reflection would have swapped the sides; a turn never does.
Answer: The kite points the way the last picture shows: turned a quarter turn clockwise, with its left and right sides NOT swapped — a reflection would have flipped it like a mirror image.
Try one yourself
The picture shows a regular hexagon — all sides and angles equal. How many lines of symmetry does it have?
Watch out
- Turning the shape but leaving a dot behind — every feature must move by the same turn.
- Confusing clockwise with anticlockwise; always picture the hands of a clock moving from 12 to 3 for a clockwise quarter turn.
- Accepting a mirror flip as a rotation: a reflected shape has its left and right swapped, so it can never match by turning alone.
Quick check
Try these on your own first — then reveal each answer.
1. The shape on the left is placed against the dashed mirror line. Is the picture on the right a reflection of it, or just the same shape turned?
2. The pennant on the left is turned 180° (a half turn). Which picture shows it afterwards — the one drawn here on the right, or would it look exactly the same as the start?
Practise this concept
Reading is the first step — the concept sticks when your child answers questions on it. Registered students practise graded questions for this lesson, with instant marking and worked explanations, and the lesson is marked complete in their progress.