HA means that the hypotenuse and the acute angle of two triangles are congruent. This does prove congruence.
LL means if two legs of two triangles are congruent, the two hypotenuses are congruent. This is similar to SSS congruence which proves congruence.
LA : Since we have two right triangles, three angles of the triangle and a side are congruent. By ASA, the right triangles are congruent.
