Proof the sum of angles of a triangle is 180 degrees

[@DigitalGnosis]

Now do it on a curved plane

[@Mulkek]

That's an interesting idea! On a curved plane (like a sphere), the sum of the angles of a triangle is actually greater than 180 degrees. This is because the geometry on a curved surface is different from flat (Euclidean) geometry (e.g., Sum of angles = 180° + excess due to curvature). Exploring triangles on curved surfaces is a fascinating topic, thanks for the suggestion 😇

[@LGamingJo]

but we can prove by simple cut a square by have am i right?

[@Mulkek]

That's an interesting and great question! If you're referring to dividing a square diagonally into two triangles (I assume you meant 'half' instead of 'have'), you're absolutely correct because the angles of the square sum to 360∘, and each triangle has angles that add up to 180∘. However, if we don’t already know that a square’s angles sum to 360∘, it’s better to start with a triangle, as it’s the simplest polygon. Once we know the sum of a triangle's angles is 180∘, we can extend that to other polygons like squares, rectangles, pentagons (5-sided polygons), hexagons (6-sided polygons), or any other type of polygons by dividing them into triangles. Let me know your thoughts! 😇