# AA Triangle Similarity Theorem

- Author:
- carabo18, Tim Brzezinski

- Topic:
- Angles, Congruence, Similar Triangles, Triangles

The

**AA Triangle Similarity Theorem**states:*If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar. Recall that "congruent" means "the same" or "of equal measure".*Below is a visual applet tool that was designed to help you prove this theorem true. Read the following instructions so you understand how the applet works! 1) You will need to scroll down to the applet and slowly drag the “Slide Me Slowly!” slider.**Pay attention to the text that pops up AND what happens to the triangle as you slide the slider**. 2) Notice that the applet considers triangles in different positions and of different sizes that have two congruent angles. 3) After fully dragging the slider to the right and noticing what happens, press the “Reset” button and play around with the applet. Change the size of the initial triangle and its position by moving the green vertices, and then slide the slider again. 4) Repeat as desired and until you feel like you can answer question 4 on the worksheet, which asks you to explain why this applet supports the AA triangle similarity theorem, which states that if two triangles have two congruent angles, then the triangles are similar.