This paper folding activity shows four methods of folding a square paper showing creases forming an equiangular or equilateral triangle. You can present this task as a problem.

Problem: Fold a square paper so that the creases show an equilateral or equiangular triangle. (An equilateral triangle is a triangle with equal sides and that it is also equiangular hence each angle is 60 degrees.)

The expected solutions are shown below. Ask the students to prove or explain why the triangles formed are equilateral triangles.

You will need at least 5 squares for this activity. The figure at the right shows how you can make one from a rectangle.

###### How to make an equilateral /equiangular triangle

Method 1.

You need two square paper for this method. Fold one square so that you have a rectangular paper which you will use as ‘ruler’ to measure 1 unit.

Method 3.

Method 4

Extension activity

- Construct using compass and straight edge the equilateral triangle formed in methods 3 and 4.
- If the side of the square is 1 unit, what is the perimeter and area of the triangle?
- Is this the biggest equilateral triangle you can make from the unit square? Use paper folding to construct the biggest equilateral triangle possible.

Reference

Ronda, E. (1999). *Developing thinking skills*. In E. Gallos et al. *Sourcebook on Practical Work for Teacher Trainers. High School Mathematics 3 and 4. Volume 2*. Published by UP NISMED.

The sourcebook is available in UP NISMED Bookstore.

This is an interesting activity. At first, I would have performed method #3, but had never considered any other the other alternatives. I sense that you can make a larger equilateral triangle, but without getting a pad of paper to try things, I don’t see an easy way of obtaining it…