Bigger angle ↔ longer opposite side

Dependencies: Base angles of an isoceles triangle are equal, Exterior angle > either non-adjacent interior angle, SAS congruence.

Statement

Let $\triangle ABC$ be any triangle. Then within the same triangle, the larger interior angle is opposite the longer side, and conversely — formally:

Intuitively: replacing each "angle" with "the side opposite it" preserves the direction of the inequality.