Thank you for the opportunity to help you with your question!
Angle-Side-Angle can be used to prove similarity and then congruence. ASA 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.
This 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.