SIMILARITY OF TRIANGLES
What actually is similarity ?
It just means that the angles are same. So two triangles are similar if all three angles of first triangle are equal to the three angles of the second triangle.
Suppose I say that the two angles A & B of first triangle are equal to the two angles say P & Q of the second triangle, then it is obvious that the third angle of both will be same because the sum of angles in triangle is 180.
That is why it is enough to say Angle-Angle theorem (AA) and not AAA.
We here must also note that the ratio of sides of triangles is same corresponding to the equal angles.
We must also be aware that capital letters are used for angles and small letters are used for the sides.
So if A=P, B=Q & C=R, then we will have a/p = b/q = c/r
Suppose this ratio turns out to be one. Then these become congruent triangles.
Another way to show similarity is SAS, in this the two sides of the two triangles are in same ratio and the angle included between them is equal. This becomes the SAS theorem (Side Angle Side).
Source : khanacademy.org