Skip to content
Smartable Academy
Smartable tools

← Symmetry

Your progress

Checking your sign-in…

Who's learning?

Each profile keeps its own read lessons, badges, streak, and practice scores on this device.

Lesson 3 of 9

How many fold lines?

Show on a big screen

5 min

Text size

Is one fold line all a shape can have? No. Some shapes have none. Some have endless fold lines.

Test properly to count properly

Draw many lines through a shape's middle. Fold along each one. Keep the lines that pass, where both halves match. That count is real, not guessed.

Fold lines found by testing, shape by shape
ShapeFold lines
A triangle with three different sides0
A triangle with two equal sides1
A rectangle2
A triangle with three equal sides3
A square4
A six-sided shape with all sides and all corners equal6
A circlethe count never stops
Figure 1 — every dashed line here passed the fold test. The rectangle's two run through the middles of its sides, not corner to corner.

A circle has endless fold lines. Any line through its centre is one. Test 12 lines — all 12 pass. Test 180 — all 180 pass too.

Watch out!

"More sides must mean more fold lines" — not always. A rectangle has 4 sides and 2 fold lines. A triangle with 3 equal sides has one side fewer. But it has one fold line more.

Turn the dashed line in the lab. Drag it round the shape, or use the slider. See if the fold works. Count the lines that work. Tap Next shape to try another. The circle never runs out of fold lines.

Loading lab…

Try the lab to finish this lesson.