Here we explore a pair of triangles where all of the sides are proportional, so that the lengths of all corresponding sides of the second triangle are a constant times the corresponding lengths of the original triangle. We want to see if this makes the triangles congruent. The construction follows the given information. Explore to see if the corresponding angles are congruent and thus the two triangles are similar.[br][br]The proof of this result is also given. Slide the slider slowly to see the steps of the proof one at a time.[br][br]