Fold an Equilateral Triangle of a Given Side Length
A few projects require you to fold an equilateral triangle. Here is one method to fold an equilateral triangle if you want to make one side the width of your paper.
Start with the paper as wide as you would like one side of your triangle to be and taller than you will need. The base of the triangle will be the bottom edge of the paper.
Fold the paper in half to create a crease perpendicular to the base of the equilateral triangle. Open the paper again.
Lift the bottom right-hand corner up to the crease keeping the bottom left-hand corner flat on the table. Crease.
Fold the top of the paper down to mark the point on the crease where the base reached. This intersection is the vertex of the equilateral triangle.
Open the paper.
Fold so the crease goes through the bottom left-hand corner and the intersection of the vertical and horizontal lines.
Repeat with the other corner.
If you remember your high school geometry, you might be able to verify the validity of this construction. Any point on the perpendicular bisector of a segment is equidistant to the endpoints of the segment. The vertical fold is a perpendicular bisector so we are certain that the triangle created is at least an isosceles triangle. Measuring the point on that crease by folding the base over to the crease ensures that not only is the triangle isosceles, but that it is equilateral.