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You can prove these triangles congruent by their corresponding angles, <b=<a, <2=<1, and <c=<c. You can also prove that these triangles are congruent because they have sides of the same length. 

It is proved by SAS postulate. (Side angle side) 
They give you information on the angle, <1=<2. 
If you see that two corresponding sides on the triangles are congruent as well, then you have your two sides and the angle to prove it congruent. 
 
You can also prove it by ASA. which is the opposite (angle side angle) You prove that two corresponding angles are congruent, such as <b=<a and <1=<2, then you prove that one corresponding side is congruent on the triangles.