Why are triangles used in bridges and roof trusses?

Because a triangle cannot change shape without one of its sides changing length. Push on a four-sided frame and it folds into a parallelogram with every member still exactly as long as it was; do the same to a triangle and nothing moves unless something actually stretches, compresses or breaks. It is the only polygon that is rigid by its geometry rather than by its joints.

That lets a structure be built from members carrying only tension or compression along their length, with pinned joints that do not need to resist bending. Materials are enormously stronger in pure tension and compression than in bending, so a truss holds far more load for far less material - which is the whole reason bridges, roofs, cranes, pylons and bicycle frames look the way they do.

It is also why a square gate sags and a diagonal brace fixes it, and why scaffolding is covered in diagonals that look redundant. The engineering term for a frame with just enough members to be rigid is statically determinate, and adding more makes it stronger but also means the load distribution can no longer be worked out from the geometry alone - which is a real problem when something is damaged and you need to know what is now carrying what.