Let two trianglesand are similar, so that the pairs of their corresponding sides and , and , and and are proportional with the same (common) coefficient of proportionality. Now consider two corresponding medians and . Consider the triangles and . They have two pairs of proportional sides and , and with the same coefficient proportionality. For the last pair, and , it is true because these segments are halves of the corresponding sides and . The angles L and L between these proportional sides are congruent, as they are corresponding angles of the similar original triangles. Thus the triangles and have two pairs of proportional sides and the congruent angles between them. According to the SAS-test of similarity for triangles, these triangles are similar. Therefore, their sides and are proportional with the same coefficient of proportionality. It is exactly what has to be proved, since and are the corresponding medians of the original triangles.