Note that the exercise states that it's a "square" pattern. If we isolate a single tile, we know that it will have four congruent sides and four right angles.
As we can see, both triangles share the same hypotenuse which means we can by the Reflexive Property of Congruence claim that this side is congruent as well. At the same time, we will remove a couple of angles that are not a part of either triangle.
Now we have a few options to choose from in order to prove congruence:
We can use that the all sides in one triangle are congruent to their corresponding sides in the other triangle. This is called the SSS Congruence Theorem.
We can also use that a leg and the hypotenuse of one right triangle is congruent to the leg and hypotenuse of another right triangle. This is called the HL Congruence Theorem.
