How do you know if a two triangles are congruent?

Answer 1

There are 4 tests that can be used, depending upon what you have:

1) SSS (Side-Side-Side) - all three corresponding sides of the triangles are equal.

2) AAS (Angle-Angle-Side) - two corresponding angles and one corresponding side are equal

3) SAS (Side-Angle-Side) - two corresponding sides and the *ENCLOSED* angle are the same

4) RHS (Right angle-Hypotenuse-Side) - The triangles are Right-angled with Hypotenuse and corresponding side equal

In test 2, if two angles are given then the third angle can be calculated, thus the order does not matter and ASA(Angle-Side-Angle) is equivalent and also proves congruency.

Note the importance in test 3 that the angle is enclosed between the corresponding sides. If it is not enclosed, the triangles may be congruent, but they may also NOT be congruent. In this case the test you are using is Angle-Side-Side (ASS - which is what you would be to say that the triangles are congruent).

Note that RHS is a special case of ASS (the only one which guarantees congruency) in that the angle MUST be a right angle (90°); this means that the third side of both triangles can be calculated using Pythagoras and RHS is effectively SSS.