In the class of "bisector of angle", the teacher asked the students to practice a problem. The figure of the problem is shown in the figure. BD in the figure is the bisector of ABC. While the students were busy drawing and analyzing the problem, Xiaoying suddenly said excitedly: "I have a discovery!" Originally, she felt that she had created a method to draw the acute bisector in a right triangle. Her method is as follows: take a point E on AB, make be = BC, and then draw de ⊥ AB and AC at point D, then BD is the bisector of ∠ ABC? Please give reasons

In the class of "bisector of angle", the teacher asked the students to practice a problem. The figure of the problem is shown in the figure. BD in the figure is the bisector of ABC. While the students were busy drawing and analyzing the problem, Xiaoying suddenly said excitedly: "I have a discovery!" Originally, she felt that she had created a method to draw the acute bisector in a right triangle. Her method is as follows: take a point E on AB, make be = BC, and then draw de ⊥ AB and AC at point D, then BD is the bisector of ∠ ABC? Please give reasons

Right. The reasons are as follows: ∵ ed ⊥ AB, ∵ bed = 90 ° in RT △ BCD and RT △ bed, ∵ BD = bdbe = BC, ≌ RT △ BCD ≌ RT △ bed (HL), ∩ CBD = ∩ EBD, ∩ BD is the bisector of ∠ ABC