Knowledge of triangles In the triangle ABC, BC = a, AC = B, ab = C. if the triangle ABC is not a right triangle, but an acute triangle or an obtuse triangle, please analogy Pythagorean theorem, try to guess the relationship between the sum of squares of a and B and the square of C, and explain the reason

Knowledge of triangles In the triangle ABC, BC = a, AC = B, ab = C. if the triangle ABC is not a right triangle, but an acute triangle or an obtuse triangle, please analogy Pythagorean theorem, try to guess the relationship between the sum of squares of a and B and the square of C, and explain the reason

First of all, let's look at the regular triangle. If the triangle is AAA, then a ^ 2 + B ^ 2 > C ^ 2
It is speculated that the sum of squares of acute triangle a and B is greater than the square of C
Look again at the 120 ° equilateral triangle
Three becomes (2a) (2a) (2 radical 3 A), so 8A ^ 2 is better than 12a ^ 2, a ^ 2 + B ^ 2