## Matching Triangles

These triangles belong to three different families.

All the triangles in a family are the same shape.

But they may not be the same size or the same way up.

Can you sort them out and explain how you did it?

You may want to use this interactivity to sort the triangles:

**If you can see this message Flash may not be working in your browser**
**Please see http://nrich.maths.org/techhelp/#flash to enable it.**
Or you could print off pictures of the triangles (

here as a Word document or

here as a pdf), then cut them out and sort them practically.

### Why do this problem?

This activity is a good one to try with young children once they are familiar with the properties of a triangle. Often, they associate the name "triangle" with a shape in a particular orientation and this problem is an excellent way to challenge this assumption. Other children may dismiss all three-sided shapes as
triangles without looking at their other attributes. The activity will require pupils to look carefully at each shape and scrutinise its properties.

### Possible approach

You could start by asking the group to tell you what they know about triangles. You could then ask one child to draw a triangle on the board and ask someone else to draw a different triangle. Invite the group to talk about what is the same and what is different about them. In this way, the discussion will include shape, size and orientation, but you could draw some triangles yourself to
bring out certain aspects.

Next you could show the group the interactivity on an interactive whiteboard or show them the triangles on

these sheets. (The first page has the triangles in colour, the second in black and white so that it can be photocopied.)
After this you could encourage the group to work in pairs so that they are able to talk through their ideas with a partner. This could be done at a computer or using the sheets of triangles to cut out and sort. Listening to their justifications can reveal a lot about their understanding of similar triangles, even though this terminology is not used.

### Key questions

What do you see if you turn this triangle round? Do the two look the same shape now?

What is the difference between these two triangles and what is the same?

### Possible extension

Children could draw their own families of triangles and label the differences and similarities.

### Possible support

Use

one of these sheets so that the triangles can be cut out, then rotated and placed on top of one another. (The first page has the triangles in colour, the second in black and white.)