Drag triangle ABC, where A is the included-angle vertex, drag D to move the second triangle, drag E to rotate it, or use the scale slider. The second triangle DEF is built with only two facts forced: the angle at D equals the angle at A, and the two sides DE and DF are k times the sides AB and AC. The theorem guarantees the rest follows automatically — the third side comes out k times BC, and the remaining angles match — so every side ratio equals the same k and the triangles are similar. Toggles show all side lengths and all equal angles. An info button opens a drawer explaining the theorem.