These type of triangles are known as isosceles right triangles.
The "isosceles" portion is due to the congruent base angles (45 degrees each). The congruent sides are opposite the congruent base angles.
The right triangle is because of the 90 degree angle.
There are infinitely many such triangles possible because we can scale the triangles however we want. We can grow or shrink them as shown in the diagram below.