Thales' theorem – parallel lines in a triangle

MathematicsPlane GeometryAges 13–14

Triangle ABC with a line DE crossing sides AB and AC. Drag D along AB (E follows so that DE ∥ BC) to see the ratios AD/DB = AE/EC and AD/AB = AE/AC stay equal. Switch to free mode to drag D and E independently and test the converse: when the two ratios are equal, DE ∥ BC. All three vertices of the triangle can be dragged too.