如图,AE、OB、OC分别平分∠BAC、∠ABC、∠ACB,OD⊥BC,求证:∠1=∠2.
问题描述:
如图,AE、OB、OC分别平分∠BAC、∠ABC、∠ACB,OD⊥BC,求证:∠1=∠2.
答
证明:∵AE、OB、OC分别平分∠BAC、∠ABC、∠ACB,
∴∠1=
∠ABC+1 2
∠BAC=1 2
(180°-∠ACB)=90°-1 2
∠ACB,1 2
∠2=90°-
∠ACB,1 2
∴∠1=∠2.