As shown in Figure 7-11, in the known triangle ABC, ad is perpendicular to D, BC is equal to D, AE is equal to ∠ BAC (2), if ∠ B ＞ C, try to explain ∠ DAE = 1 / 2 (∠ B - ∠ C)

As shown in Figure 7-11, in the known triangle ABC, ad is perpendicular to D, BC is equal to D, AE is equal to ∠ BAC (2), if ∠ B ＞ C, try to explain ∠ DAE = 1 / 2 (∠ B - ∠ C)

∠DAE=90°-∠AED
=90°-（∠EAC+∠C）
=90°-（∠BAE+∠C）
=90°-（∠BAD+∠DAE+∠C）
=90°-（90°-∠B+∠DAE+∠C）
=∠B-∠DAE-∠C
That is, DAE = 1 / 2 (∠ B - ∠ C)

In △ ABC, ∠ B ＞ C, ad is the height on the side of BC. AE is the bisector of ∠ ABC, which indicates that ∠ DAE = 1 / 2 (∠ B - ∠ C)

(there is a problem with your title, "AE is the bisector of ∠ ABC" should be changed to "AE is the bisector of ∠ BAC"?) it is proved that: ∵ △ ABC has ∠ B and ∠ C, ad is the height on the side of BC. AE is the bisector of ∠ ABC. ∵ BAC / 2 = ∵ EAC = (180 - ∵ B - ∵ C) / 2, and ∵ DAC = 90 ° - ∵ C ∵ DAE =