# SAS Similarity Theorem

- Author:
- powere, Tim Brzezinski

- Topic:
- Congruence, Similar Triangles, Triangles

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****. In the***a*and*b***pink triangle**, the**black angle is the included angle between sides**. Interact with the applet below for a few minutes. As you do, be sure to move the locations of the*ka*and*kb***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!**