Israel claims that all 45degree right triangles are similar. Is he correct? Explain.

Alrity ... well, a right triangle with a 45°, will also have a third angle of 45°, and thus all three angles will then be 45°, 45° and 90°, for all right-triangles, and they'd be similar by AA anyway. So all right-triangles with a 45°, will have another 45° angle and a 90° one, and the three angles will then be the exact same value for all right-triangles with one 45°. Thus all would then be similar by AA.