如图,已知△ABC中,∠B大于∠C,AD为∠BAC的平行线,AE⊥BC,垂足为E。求证:∠DAE=二分之一(∠B-∠C)

2025-06-22 01:41:10
推荐回答(2个)
回答1:

∵AD平分∠BAC
∴∠BAD=∠CAD=1/2∠BAC=1/2(180°-∠B-∠C)=90°-1/2∠B-1/2∠C
∵AE⊥BC
∴∠BAE=90°-∠B
∴∠DAE=∠BAD-∠BAE
=90°-1/2∠B-1/2∠C-90°+∠B
=1/2(∠B-∠C)

回答2:

∠DAE = 1/2∠BAC - ∠BAE
=1/2(180-∠B-∠C) - (180-90-∠B)
=90-1/2∠B-1/2∠C-90+∠B
=1/2(∠B-∠C)