Answer: See the diagram below for the drawing.
Triangle E''EF is a right triangle since one angle is 45+45 = 90 degrees. Also, the triangle is isosceles because EF = E''F. Rotation doesn't change the length of a segment. You can imagine instead of rotating a segment, you rotate the camera instead, and that means the segment is untouched and remains the same length. So that's why EF and E''F are the same length.
Since we have an isosceles right triangle, this means we have a 45-45-90 triangle. The three values mentioned are the angles of the triangle. Another property of this triangle is that segment E'F bisects segment E''E. Also, segment E'F bisects angle EFE''.