Question

When we draw a general triangle, we're inclined to draw a triangle that's either right, or acute, or obtuse, but not the general triangle itself. Then how do humans know its existence?

Answer 1

Humans recognize the existence of a general triangle through the fundamental definition in geometry. While we may visualize specific types of triangles, all triangles share the property of having three angles totaling 180 degrees. We use this knowledge in various mathematical and physical applications, such as the Pythagorean theorem and trigonometry.

Step-by-step explanation:

Humans know the existence of a general triangle through the definition and properties established in geometry. A triangle must be a three-sided figure lying on a plane, with the sum of its three angles adding up to exactly 180 degrees. This definition is independent of whether the triangle is right, acute, or obtuse. In our visualizations, we tend to default to familiar shapes, but the concept of a triangle encompasses all variations adhering to the basic geometric principles. For example, the Pythagorean theorem, which states that a² + b² = c² for right triangles, relies on this understanding of a triangle's fundamental properties. Similarly, when analyzing forces in physics or determining distances, the properties of triangles are used to apply trigonometry and geometric reasoning.