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 Description  
 Angle-Angle (AA- Similarity):  If two angles of one triangle are congruent to two corresponding angles in another triangle, then the triangles are similar.
For example, in the figure below there are two triangles: a larger triangle, ABC, and a smaller triangle, ADE. Angles ADE and ABC are corresponding because they both lie in the same relative position in the two triangles. Angles ABC and AED are not corresponding since they do not lie in the same relative position in the two triangles. For the same reason, sides AE and AC are corresponding while sides BC and AD are not.



In the figure above, we are given that DE is parallel to BC. Then the triangles ADE and ABC are similar by Angle-Angle. This is true because angle ADE is congruent to angle ABC because they are corresponding angles, and angle EAD and angle CAB are congruent since they are identical.