SAS Similarity Theorem
In the applet below, you'll find two triangles. The black angle in the green triangle is congruent to the black angle in the pink triangle. In the green triangle, the black angle is the included angle between sides a and b. In the pink triangle, the black angle is the included angle between sides ka and kb. Interact with the applet below for a few minutes. As you do, be sure to move the locations of the green triangle's BIG BLACK VERTICES and the location of the BIG X. You can also adjust the value of k by using the slider or by entering a value between 0 & 1.
Notice how these two triangles have 2 pairs of corresponding sides that are in proportion. (After all, as long as a > 0 & b > 0, ka/a = k and kb/b = k, right? ) The BLACK ANGLES INCLUDED between these two sides ARE CONGRUENT as well. From your observations, what can you conclude about the two triangles? Why can you conclude this? Clearly justify your response!