Triangle congruence and similarity criteria


Congruence criteria:

| Criterion | Description                                     |
|-----------+-------------------------------------------------|
| SSS       | All three corresponding sides are same.         |
|-----------+-------------------------------------------------|
| SAS       | Two corresponding sides                         |
|           | *and the angle between them* are same.          |
|-----------+-------------------------------------------------|
| ASA       | Two corresponding angles                        |
|           | and the side between them are same.             |
|-----------+-------------------------------------------------|
| AAS       | Two corresponding angles                        |
|           | and an angle that is not between them are same. |
|-----------+-------------------------------------------------|
| HL        | For right triangles, if hypotenuse              |
|           | and one other side are same.                    |

(SSA is doesn't always hold and can't be used generally)

Similarity criteria:

| Criterion | Description                               |
|-----------+-------------------------------------------|
| AA        | Two corresponding angles are same.        |
|-----------+-------------------------------------------|
| SSS       | All corresponding sides are proportional. |
|-----------+-------------------------------------------|
| SAS       | Two corresponding sides are proportional, |
|           | and the angle between them are same.      |

In the case of similarity criteria, when two side are proportional, the constant of proportion should be same as well.

Reference: Khan Academy