Here are three triangles. One has all its sides the same length, one has two sides the same, and one has no two sides the same.

What is the same about all three of them? And what is different?

Three triangles are shown sorted into their families by the length of their sides. Notice how many sides match each time, and that the last one is still the same family when turned on its side.

Today we sort triangles into their three families. One pupil comes to the board to drag a triangle. Before they drag, everyone watching says which sides they think match — then the pupil drags it to the right family: equilateral, isosceles or scalene.

Now we make triangles with strips of paper or lollipop sticks. Work through these in order:

• Make a triangle with all three sides equal.
• Make a triangle with exactly two sides equal.
• Make a triangle with no two sides equal.
• Try to make a triangle with sides of 3 cm, 3 cm and 7 cm.

What we learned today

• Every triangle has three sides — the side lengths sort it into a family.
• All three equal is equilateral, exactly two equal is isosceles, none equal is scalene.
• An equilateral triangle does have two equal sides too — but because all three match, we give it the strongest name, equilateral.
• Turning a triangle never changes its family.

Coming up

Next we look at four-sided shapes — squares, rectangles, rhombuses and more — and sort them by their sides and corners too.