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.