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Symmetry

Track quiz

One table first, then seven questions.

Symmetry — what to fold, what to turn, and what each one tells you
IdeaWhat to remember
Fold and matchA line of symmetry lands the shape exactly on itself. Flipping a point across it is a reflection.
Not every middle lineEqual halves are not matching halves. A middle line still has to pass the fold test.
How many0 for a triangle with three different sides, 2 for a rectangle, 4 for a square, never-ending for a circle.
Symmetry around usLetters fall into four groups: up and down, flat across, both, or neither.
TurningOrder counts the matching turns in a full circle. Turning symmetry can come with no fold line.
Complete itEach missing square sits in the same row, the same distance the other side of the line.

A shape is folded along a drawn line. When does that count as a line of symmetry?

  • It is enough that the two halves have the same space inside.
  • One half must land exactly on the other, with nothing sticking out.
  • It is enough that the line passes through the middle.

A rectangle is 8 cm long and 5 cm tall. Is the corner-to-corner line a line of symmetry?

  • Yes — it cuts the rectangle into two equal pieces.
  • No — most of the edge lands off the shape when folded.
  • Yes — it passes through the middle of the rectangle.

How many lines of symmetry does a square have?

  • 2
  • 4
  • 8

You test 12 lines through the centre of a circle. All 12 pass. You test 180, and all 180 pass too. What does that tell you?

  • The test is broken — a shape cannot have that many.
  • A circle's fold lines never run out. You can always draw one more.
  • A circle has exactly 180 lines of symmetry.

Which of these capital letters has no fold line at all?

  • H
  • F
  • T

A leaning shape has no line of symmetry. Turn it 180°, and every part lands back on the shape. What is true?

  • It cannot really have no line of symmetry. It turns onto itself.
  • It has turning symmetry of order 2, and no fold line. The two are separate things.
  • Turning it 180° is the same as folding it.

A filled square sits three squares left of the fold line. Where does its partner go?

  • Three squares further left, in the same row.
  • Three squares to the right of the line, in the same row.
  • Directly on the fold line.

Chapter 9 of your textbook is called Symmetry. Go and read it now. You have folded every idea in it already. So its figures will look familiar.

Next: The Other Side of Zero. Numbers below zero. And a number line that keeps going the other way.

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This track

  1. 0 Start here
  2. 1 Fold it, and it matches
  3. 2 Not every middle line
  4. 3 How many fold lines?
  5. 4 Symmetry around us
  6. 5 Matching partway through a turn
  7. 6 Half a picture decides the rest
  8. 7 The big picture
  9. 8 Track quiz

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