SSS SAS AA How do you use corresponding sides and angles to determine the similarity of triangles?

Congruent angles When a line is intersected by a pair of parallel lines, congruent angles are formed.

Angle, Angle (AA) http://www.mathopenref.com/similaraaa.html

Side, Side, Side (SSS) If all three sides in one triangle are in the same proportion to the corresponding sides in the other, then the triangles are similar. So, for example in the triangle above, the side PQ is exactly twice as long as the corresponding side LM in the other triangle. PR is twice LN and QR is twice MN. All three sides are in the same proportion, in this case 2:1 (two to one), and so the triangles are similar. http://www.mathopenref.com/similarsss.html

Side, Angle, Side (SAS) http://www.mathopenref.com/similarsas.html