The transversal is parallel to a side of the triangle

Drag point D or point A.[br]The two indicated ratios remain equal to each other.[br][br]This way of showing equal ratios is often called Thales Theorem. It can be proved using the similar triangles ABC and ADE.[br][br]The parallel transversal divides the two sides of triangle ABC proportionately.[br][br]The next diagram in this sequence shows the case of a non-parallel transversal.