If we are talking about triangles forming bridges as in trusses, then the regular repeated arrangement of triangles allows the elements that make them experience purely axial loads and not bending moments of any real significance. read more
Triangles have been used extensively throughout history in construction due to their rigid shape and strength. Unlike a square, that can shift into a parallelogram when force is applied to one of its sides, an equilateral triangle's sides and angles are fixed. read more
Triangle tend to make strong frameworks. Suppose the these three represent bridges made from toothpicks. Which will hold the most weight on top without breaking or shearing to the left or right. read more
To understand why triangles give a stronger structure than squares or rectangles, you need to imagine a square with a hinge at all 4 of its corners, and a triangle with a hinge at all 3 of its corners. read more