Grade by Grade
D. Structures and Mechanisms · Form and Function

Symmetry in Structures

D2.4 D2.2 A1.5About 40 minutes
Learning goals
  • I can identify line symmetry and rotational symmetry in built and natural structures.
  • I can explain how symmetry helps a structure share loads evenly and stay balanced.
  • I can describe how designers keep an asymmetrical structure stable.

Words to know

symmetry
When one part of a shape or structure matches another part exactly after a flip or a turn.
line of symmetry
A line that divides a shape into two halves that are mirror images.
line symmetry
A shape has line symmetry if it can be folded along a line so the two halves match exactly. Also called reflective or mirror symmetry.
rotational symmetry
A shape has rotational symmetry if it looks the same after being turned less than a full turn around its centre.
asymmetrical
Not symmetrical: the parts do not match.

Hook: fold it and see

Fold a sheet of paper in half, cut out half of a maple leaf shape along the fold, and open it up. Both sides match perfectly.

Now look at pictures of bridges, towers, chairs, airplanes, tipis and hockey nets. Most of them look almost the same on both sides. Builders don't do this just because it looks nice. Symmetry helps structures handle forces.

A steel arch bridge over a calm river, seen straight on, with autumn trees on both banks and its reflection in the water.
Fold this bridge down the middle and the two halves match. Symmetry spreads the load evenly to the supports on each side. AI-generated image

Remember from math

In math class you learned about line symmetry (a shape folds onto itself along a line) and reflections (flips). In Grade 7 science you will use these ideas to explain why so many structures are symmetrical.

Two kinds of symmetry in structures

  • Line symmetry: a line divides the structure into two mirror-image halves. Examples: a ladder, a chair, a suspension bridge, an airplane seen from above, a hydro tower seen from the front, the human body (on the outside).
  • Rotational symmetry: the structure looks the same after part of a turn around its centre. Examples: a bicycle wheel, a round dome, a tipi seen from above, a stool with 3 or 4 identical legs, a snowflake.

Nature is full of symmetry too: butterflies, snowflakes, many leaves and flowers, and animal skeletons.

line of symmetrywater
A suspension bridge is symmetrical about a vertical line through its middle. Each tower and cable on one side matches one on the other side, so the loads on both sides are shared evenly. Not to scale.

Why symmetry helps

  1. Balanced loads: in a symmetrical structure, the load on one side is matched by an equal load on the other side, so the forces are shared evenly between matching parts.
  2. Centre of gravity in the middle: a symmetrical structure (made of the same material on both sides) has its CG on its line of symmetry, usually right over the middle of its base. That helps stability.
  3. Easier to design and build: engineers can design one half and copy it. Matching parts (like identical legs) can be made in a factory all the same way.
  4. Even response to forces: a symmetrical airplane, rocket or canoe moves straight and steady through air or water, because forces on both sides are equal.

When structures are asymmetrical

Some structures are asymmetrical on purpose: a balcony sticking out from a wall, a crane, a cantilevered roof, a sign hanging off one side of a pole. Designers keep them stable with counterweights, strong anchors into foundations or walls, and extra-strong parts where the load is uneven.

Worked example

Let's find symmetry

Which kind of symmetry does each structure have? (a) a ladder seen from the front, (b) a bicycle wheel, (c) a four-legged stool seen from above, (d) a teapot seen from the side.

  1. (a) A ladder's left rail matches its right rail: line symmetry, with a vertical line down the middle.
  2. (b) A bicycle wheel looks the same after turning it by the space between two spokes: rotational symmetry.
  3. (c) Turn the stool a quarter turn and it looks the same: rotational symmetry (it also has lines of symmetry).
  4. (d) The spout is on one side and the handle on the other: asymmetrical from the side.

(a) line, (b) rotational, (c) rotational (and line), (d) none: asymmetrical.

Worked example

Let's explain an asymmetrical design

A balcony sticks out 2 m from the wall of an apartment building, with no posts underneath. Why doesn't it fall?

  1. The balcony is asymmetrical: all of its load (the balcony itself plus people) is on the outside of the wall.
  2. That load tries to rotate the balcony downward around the edge of the wall.
  3. The balcony slab is anchored deep into the building's floor (the floor slab continues inside), and the weight of the building above helps hold the inside end down, acting like a counterweight.
  4. Steel bars in the concrete, near the top of the slab where it is stretched, resist the tension.

It is anchored into the building, which balances the outside load; this is how designers make asymmetrical structures stable.

wallbuilding above presses downbalcony load (people, snow)load tries to rotate it down heresteel bars near the top(the top is stretched)
An asymmetrical balcony: the slab continues inside the building, where the weight of the floors above holds it down. Steel bars near the top of the slab resist the tension.
Just for fun

Paint half a butterfly on one side of a sheet of paper, fold it in half and press. Open it up: instant line symmetry, and you only had to paint half!

Hands-on activity

Symmetry and balance test

You need: thin cardboard (cereal box), scissors (grown-up help), a pencil, a ruler, and a pushpin with a plumb line from the centre-of-gravity lesson (optional).

  1. Fold a piece of cardboard in half and cut out a symmetrical bridge or tower shape along the fold. Open it up. Draw the line of symmetry along the fold.
  2. Cut out a second shape that is asymmetrical (for example, a tower with a long arm on one side, like a crane).
  3. Try to balance each shape on its base on the table, then on a pencil tip. Where is each one's centre of gravity?
  4. Add a paper-clip "counterweight" to the short side of the crane shape until it stands up on its base.
  5. Go on a symmetry hunt at home. List 5 structures with line symmetry, 3 with rotational symmetry, and 2 that are asymmetrical. For the asymmetrical ones, explain what keeps them stable.

What to look for: the symmetrical shape's CG is on the fold line; the crane shape tips toward its long arm until a counterweight is added. Hunt answers: line: chair, bed, window, door frame, table; rotational: fan, wheel, round table, ceiling light; asymmetrical: floor lamp with a curved arm (heavy base), wall shelf (anchored with screws).

Your turn

1

What is a line of symmetry?

2

Give one example of a structure with line symmetry.

3

Give one example of a structure with rotational symmetry.

4

Where is the CG of a symmetrical structure made of the same material on both sides?

5

How does symmetry help a structure share loads?

6

Name two ways designers keep asymmetrical structures stable.

More practice: warm-up

1

Is a butterfly symmetrical?

2

Does a snowflake have rotational symmetry?

3

What does asymmetrical mean?

4

Is a hockey net (seen from the front) symmetrical?

5

Name one reason symmetrical structures are easier to build.

More practice: on your own

1

Why do airplanes need to be symmetrical from left to right?

2

A table has three identical legs evenly spaced. Describe its symmetry.

3

A crane is asymmetrical. Explain how its counterweight relates to the idea of balance.

4

A diving board is asymmetrical. What keeps it from tipping into the pool?

5

Explain why the CG of a symmetrical hydro tower is on its centre line.

Challenge

1

A designer wants to build a sculpture that leans dramatically to one side. Suggest two ways to keep it stable and safe.

2

Explain why a canoe with all the gear piled on one side is dangerous.

3

Many dome-shaped shelters, like an iglu, have rotational symmetry. How does this help the structure handle loads such as snow and wind?

Check your understanding

Quiz

1.

A line of symmetry divides a shape into...

2.

Which has rotational symmetry?

3.

Where is the CG of a symmetrical tower made of the same material throughout?

4.

Which is a main reason structures are symmetrical?

5.

How is an asymmetrical crane kept stable?

6.

Why must an airplane be symmetrical from left to right?

For parents and teachers

Big idea (D2.4): Students describe the role of symmetry in structures and find examples. Symmetry spreads loads evenly, keeps the centre of gravity centred (D2.2) and simplifies design and manufacturing. Asymmetrical structures need counterweights or anchors.

How to help: Go on a symmetry hunt in your neighbourhood: bridges, houses, playground equipment, hydro towers, cars. Ask: "What would happen if one side were heavier?"

Common difficulties:

  • Thinking symmetry is only about looks. Keep asking how symmetry affects forces and balance.
  • Mixing up line and rotational symmetry. Fold for line symmetry; turn for rotational symmetry.
  • Safety: a grown-up should help with scissors.