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Maths · Geometry

Preserve measure under a rigid transformation

Use the fact that translation, rotation, and reflection preserve lengths and angles.

Free to use and free to share. There is no sign-up, no score, and nothing a child does here is recorded or sent anywhere.

Practise it now

Exactly one of these readings comes out different. Which one?

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A worked example

One question of the kind this skill is tested with, worked all the way through: the reasoning, and what the wrong answers are there to catch.

Moving a shape does not resize it

See which measurements survive when a triangle is flipped, turned or slid.

  1. 23 cm
  2. 16 cm
  3. 7 cm
  4. 13 cm

Answer: 13 cm

How you get there

Being rotated a half turn about the origin moves the triangle without stretching it, which means side B'C' is exactly as long as side BC: 13 cm.

Why the other answers tempt

Only an enlargement changes lengths - and none of these moves is an enlargement.

If they are stuck, say this

Reflections, rotations and translations only change where a shape sits, so read the measurement straight off the original figure.

Now do it live in Spot the Changed Reading

What this exercise is doing

Spot the Changed Reading

Exactly one of these readings comes out different. Which one?

The programme is “Slide 4 right”, then “Slide 2 right”, then “Flip in the line x = 4”. Every move on that list picks the outline up and puts it down without changing its size or shape, so the lengths of the sides, the angles at the corners and the area inside are all exactly what they were. What a rigid motion does change is WHERE things are, and here that is the coordinates of corner A. There is one more thing a flip changes and a slide or a turn never does: the letters ran anticlockwise round the outline and now run clockwise. The exam-safe habit is to sort every reading into "about the shape itself" or "about where the shape is": the first kind always survives, the second kind is the only place an answer can hide.

  1. Step 1. Watch it move. Play the cards and watch the readings.
  2. Step 2. The odd one out. Which single reading came out different?

What to say if they get stuck

  1. Tap a reading and it is drawn twice: once on the faint outline where the shape started, once on the solid one where it is now. Scrub slowly and watch whether the two marks stay the same.
  2. A slide, a turn and a flip all pick the outline up without stretching or squashing it, so every length, every angle and the area come through untouched.
  3. A flip is the only one of the three that reverses the outline, and this programme has one of them, so the letters end up reading round the other way.

Open Spot the Changed Reading on its own page to share it

How preserve measure under a rigid transformation differs from the skills beside it

The same exercise practises several skills, and telling them apart is often the difficulty rather than the exercise itself. On this page the skill is: use the fact that translation, rotation, and reflection preserve lengths and angles, and it stops where excludes calculating an unknown measure from unrelated angle or length rules.

  • Identify a shape property

    Identify one stated property of a 2D or 3D shape. Excludes calculating measure.

  • Reflect a shape

    Identify the result of one reflection in a stated mirror line. Excludes rotation and translation.

  • Rotate a shape

    Identify the result of one stated rotation. Centre, direction, and turn are fixed.

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Questions parents ask about preserve measure under a rigid transformation

Answered from what the skill map records about this skill, not from a template. Every answer here is on the page, and the same questions are the page's FAQ structured data.

Use the fact that translation, rotation, and reflection preserve lengths and angles. It is one of 55 named maths skills in the 11+, in the geometry strand, and this page carries 1 interactive exercise that practises it.

Knowing which maths topic to practise is most of the work

A free diagnostic covers arithmetic, fractions, geometry, measure and data handling, and comes back with the topics to spend the next few weeks on.