Answer:
AAA (Angle Angle Angle) Proving that the angles are the same (Or of the same ratio if diluted), if this is true, the two figures are similar.
SSS (Side Side Side) Proving all the sides are the same size (Or again of the same ratio) also proves similarity.
SAS (Side Angle Side) If two sides and the angle in between are the same, then the triangles are similar.
Explanation:
EX)
Triangle A has sides 10, 5, and 12
Triangle B has sides 20, 10, and 24
The relationship is the same between both triangles, just that the sides are multiplied by 2. This is SSS
If Triangle A has two sides 5 and 10 with an angle of 25 degrees, then Triangle B must have that same angle alongside those two sides, or at least a consistent ratio if diluted. Proof SAS
If Triangle A and B have the same angles, they are similar.