### Rolling Triangle

The triangle ABC is equilateral. The arc AB has centre C, the arc BC has centre A and the arc CA has centre B. Explain how and why this shape can roll along between two parallel tracks.

### Turning Triangles

A triangle ABC resting on a horizontal line is "rolled" along the line. Describe the paths of each of the vertices and the relationships between them and the original triangle.

### Mystic Rose

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

# Notes on a Triangle

##### Stage: 3 Challenge Level:

Watching the film may stimulate lots of discussion about properties of triangles, symmetry and rotation.

If you want to watch it directly from the National Film Board of Canada's website, go here

You could ask students to watch it twice, then talk about what they saw in pairs before having a whole group discussion. Students might notice the different ways in which the initial triangle is split during the film and it might be handy to have some large copies of the triangle available so that they can demonstrate what they saw in the film.

This initial discussion offers a good opportunity for you to draw out well articulated descriptions.

Choose a section of the film and ask students to describe what happens there.
eg 1 - 34 seconds and 35 - 45 seconds may be two natural chunks for students to start to focus on.

What mathematical properties remain constant throughout the clip?
Students can recreate short sequences using cut-out triangles.
Here is a sheet of triangles that can be printed off and cut out.

Ask students to consider if a section of the dance can be performed by a different shape.

If the triangle is replaced with a kite, or a rhombus, or an arrowhead, or ...
can the new shape be bisected into congruent halves?
can the new shape be trisected into equal thirds?
can dissections be carried out in different ways?

Which shapes will allow the same range of movements and symmetries?