Question

如图,在三角形ABC中,AD垂直BC,AE平分角BAC,则有∠DAE=1/2(∠C-∠B),请说明理由

Answer 1

因为 ∠BAD=90-∠B 且∠A=180-∠B-∠C

所以 ∠DAE=∠BAD-1/2∠A

=90-∠B-1/2(180-∠B-∠C)

=90-∠B-90+1/2∠B+1/2∠C

=1/2∠C-1/2∠B

=1/2(∠C-∠B)