(From outside the box geometry)

Claim: The longest side in a triangle must be opposite from the largest angle

Idea: Suppose there is some line L where L is the longest side for some triangle T

Then, since neither of the remaining two sides of T can have a length greater than that of line L, the remaining one vertex of T, V, should be located among the area colored green.

Clearly, the angle opposite to line L would be at its smallest when vertex V is located at the edge of the area colored green. Clearly, when vertex V is located at any point along the edge of the area colored green, the resulting triangle would either equilateral or bilateral, with the angle at vertex V always being either bigger than or equal to all other two angles.

Clearly, these pieces be enough to prove the original claim, if properly fitted and formulated together. However, making a formal proof is a process which I'm not very familiar with. Could someone perhaps help me with this?

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