The picture given above is distorted to the point that the relative positions of the points are not correct. Compare to the more carefully drawn figure at right. Now, recall our careful wording as reproduced below. We did not say anything wrong, but the underlined words are less than candid:

The angles JBA and JAB are equal (since JAB is an isosceles triangle), the picture clearly tells you that if you subtract JBA from CBJ and and JAB from JAE you obtain ABC and BAE. Yet one of these (ABC) is a right angle, whereas the other (BAE) is obtuse by construction. How can this be?

The point J is so far out that the line JE is outside the angle AJD, not inside it, as the bad picture led you to believe...