Final answer:
In geometry, the shape of a triangle is used to determine the concepts that it has three sides and that the sum of its interior angles equals 180 degrees, which are essential properties in two-dimensional Euclidean geometry.
Step-by-step explanation:
The question pertains to two fundamental concepts associated with triangles in geometry, a branch of mathematics. Firstly, a triangle is a three-sided polygon which is a two-dimensional shape composed of straight lines, and secondly, the triangle has the property that the sum of its interior angles is always 180 degrees. This is a foundational rule applicable to Euclidean geometry, where shapes are studied in a flat, two-dimensional plane. In addition to their geometric properties, triangles can also be used in various mathematical contexts to solve problems or represent relationships between different variables, such as those shown in mathematical formulas and equations. To understand triangles, one must acknowledge both their physical representation as a shape with three sides and angles, as well as their application in expressing mathematical relationships.