As already noted it is a bit of an oversimplification to say “triangles are the strongest”. However for many materials their ability to resist compression or tension is much greater than their ability to resist bending.
For example if you wanted to break a pencil how would you do it? You would probably try to bend it in the middle until it breaks, not try to smash it from either end or just pull it straight apart.
What arranging such materials in a triangle does is make it so in order to bend one leg of the triangle you would need to either lengthen or compress at least one of the other two legs (or detach the corners, but we can ignore that). The relatively weak resistance to bending is replaced by resistance to compression or stretching.
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