A reflection in space

Liri looked at her own point in the window glass. Left and right – exactly the same.

Liri: “I’m the same on both sides! Is that important?”
Erklärus: “Very much so. It’s called symmetry – and it helps you recognise patterns in the sky, even when you see them from the other side.”

🪞 Line symmetry

A shape has line symmetry if an imaginary line – the line of symmetry – divides it into two exactly equal halves. If you fold the paper along this line, both sides lie exactly on top of each other.

🦋

A butterfly is a classic example: the red dashed line is the line of symmetry.

✂️ Mirroring a pattern

On the right, click the squares that mirror the pattern on the left – that makes a symmetrical picture:

🔺 Flat or solid?

Plane shapes are flat (2D): square, rectangle, triangle, circle. Solids are three-dimensional (3D) – they have depth and do not fit onto a sheet of paper.

🎲
Cube
6 faces, 12 edges, 8 vertices
⚽
Sphere
1 curved surface, no edges, no vertices
📦
Cuboid
6 faces, 12 edges, 8 vertices
🥫
Cylinder
2 round faces, 1 curved surface
🔺
Pyramid
5 faces, 8 edges, 5 vertices
🍦
Cone
1 round face, 1 curved surface, 1 apex
🌌 Shapes in the universe

Planets are almost perfect spheres – shaped by their own gravity.
Many satellites are shaped like a cuboid, with fold-out solar panels.
Some constellations look almost symmetrical if you draw an imaginary line through their middle.

❌ Common mistake

A square and a cube are often mixed up – but a square is flat (2D), a cube is three-dimensional (3D) and is even made of six squares!

Tip: can you pick it up and look at it from all sides? Then it is a solid (3D), not a plane shape.

🪞 Exercise 1 – Symmetry
A heart, a circle and a footprint – which of these shapes does not have line symmetry?
Heart
Circle
Footprint
🎲 Exercise 2 – Recognising solids
How many vertices (corners) does a cube have?
⚽ Exercise 3 – Everyday objects
A football has the shape of a…
Pyramid
Sphere
Cylinder

Shapes you recognise again

Liri looked at her star map once more – this time with a trained eye for shapes and reflections.

Liri: “If I see a constellation from the other side, I can still recognise it now – because of symmetry.”
Erklärus: “And if you know whether a heavenly body is a sphere or a cuboid, you also know straight away whether it could be a planet or a satellite.”
“Symmetry: a line divides a shape into two mirror-image halves. Solids (3D) are three-dimensional – cube, sphere, cuboid, cylinder, pyramid, cone – unlike flat (2D) shapes.”
What you learned today
Line of symmetry: equal + mirrored
2D: flat (square, circle…)  ·  3D: solid (cube, sphere…)
🌟

Chapter 12 mastered!

Liri now recognises reflections and knows which shapes planets, moons and satellites have.

Erklärus’s notebook – page 12:
“Symmetry: a line of symmetry divides a shape into two equal, mirrored halves. Solids (3D): cube, sphere, cuboid, cylinder, pyramid, cone – with faces, edges and vertices, unlike flat (2D) shapes.”
← Back to overview 12 – Symmetry & 3D Shapes