Equilateral triangles consist of three line segments of equal length that converge at three vertices encompassing 60-degree angles. Six equilateral triangles sharing one common vertex form a hexagon. The regularity of equilateral triangles makes the shape a favourite building block for quilt patterns and tessellations. Designers can break down most regular shapes into compositions of numerous equilateral triangles. Learning how to arrange equilateral triangles to make other shapes allows you to develop complex patterns from a simple building block.

Line two equilateral triangles up together along one edge to form a parallelogram, a shape that has four sides, each of which is parallel to the side directly opposite it.

Add another equilateral triangle to a different edge of the parallelogram to form a trapezoid, a four-sided shape with two sides that are of different lengths.

Combine two trapezoids along their long edges to form an equilateral hexagon.

Place two parallelograms together such that they mirror each other along the touching edge to form a V-shaped hexagon.

Experiment with combinations of the above composite shapes (such as a hexagon and trapezoid, or a parallelogram and a trapezoid) to create irregular shapes.