A key concept in architecture is the use of triangles. Triangles are known as the sturdiest figure in the architecture world. Architects commonly use these shapes to construct their buildings. The inequalities help prove that the shape is actually valid and can be build without causing problems. The triangles are used in the examples below:

The triangle congruence helps measure the forces applied on the building to make sure that the forces are balanced, ultimately that the building will not collapse. It will also help the architect see if the triangles match up together correctly.

The Triangle Congruences are:

- Side-Side-Side

- Side-Angle-Side

- Angle-Angle-Side

- Angle-Side-Angle

- Hypotenuse-Leg

Triangles make many of the structures that we know today. The triangles and their concepts are an essential part of Architecture.