<h3>Answer:</h3>
- DE is not included, AAS
- DF is included, ASA
<h3>Explanation:</h3>
An angle is identifiede by its vertex. A side is identified by the vertices it lies between. When the vertices are X and Y, the side that lies between (is included) is side XY.
1. The angle vertices are E and F, so the side included between them would be side EF. The named side, DE, is <em>not</em> included.
The postulate naming is pretty straightforward. Each A represents an angle, and each S represents a side. The sequence of letters matches the sequence of the parts of the geometry. Thus AAS refers to a pair of angles with the side being not between them, while ASA refers to a pair of angles with the side between.
When you have two angles and a not-included side, the postulate you must invoke is the AAS postulate.
2. The explanation of 1 pretty much covers it. Side DF is (included) between angles D and F, so the ASA postulate applies.
