Triangles

Let’s say you are at uhh.. the Taj Mahal, and you decide to take a picture. When you take your triprod out, you will probably notice that it has three legs, like a triangle. Looking around at the tourists and sometimes professionals, you find that every single triprod has a triangular base. You think triangles have this special property that makes its way into these things.

Yes, they do. You see, triangles are one of the most important things, if not the most important, in Geometry and real life. First of all, triangles are simple. Thus many formulas and theorems stem from triangles. Also, triangles are easy to tell if they are the same, or at least, similar. Unlike all other shapes, where you need to prove the sides are the same, for triangles, you only need two or even ONE side to prove congruence.

Triangles are also able to well-define certain shapes. For example, where the lines stemming from each vertex, that are the same distance away from the two sides of the vertex, intersect, you get a unique circle that fits snugly inside the triangle. Similarly, if you connect the perpendiculars to the sides that go through the midpoints, you get another circle that fits snugly outside the triangle. This is useful for proving theorems. Just like how two points define a line, in 3-D Geometry,three points(a triangle)define a plane. (A plane is a flat surface in space. ). This makes the triprods stable.

As you can see, triangles are virtually everything in Geometry.