Thank you for the opportunity to help you with your question!
The Angle-Side-Angle postulate can be used to prove similarity and then congruence.
The ASA postulate as it is called is applicable because you have the right angle
indicated by the square in the corner immediately proceeded by a side
that is congruent indicated by the single hash mark in both triangles
immediately followed by a pair of vertical angles which are congruent.
only proves similarity. However the fact that corresponding sides have
the same length sets the proportion of those sides as 1:1. All the other
sides must follow this proportion as the triangles are similar.
Triangles which are similar and have equal side lengths are congruent
triangles. Please let me know if you need any clarification. I'm always happy to answer your questions.