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
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.
- 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.
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.