Yes, two right isosceles triangles are always similar.
To understand why, let’s first define what a right isosceles triangle is. A right isosceles triangle has one 90-degree angle and two sides of equal length. This means that the two angles opposite the equal sides must each be 45 degrees (since the angles in a triangle must add up to 180 degrees).
Now, consider any two right isosceles triangles. Since both triangles will have one 90-degree angle and two 45-degree angles, they share the same angle measures. According to the Angle-Angle (AA) similarity criterion in geometry, if two triangles have two corresponding angles that are equal, then the triangles are similar. Therefore, if you have two right isosceles triangles, they will always have the same angles of 90 degrees, 45 degrees, and 45 degrees.
This similarity means that the triangles can be scaled versions of each other; they may differ in size, but their shapes remain the same. Thus, you can conclude that two right isosceles triangles are indeed always similar.