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.

证明:∵AE、OB、OC分别平分∠BAC、∠ABC、∠ACB,
∴∠1=

1
2
∠ABC+
1
2
∠BAC=
1
2
(180°-∠ACB)=90°-
1
2
∠ACB,
∠2=90°-
1
2
∠ACB,
∴∠1=∠2.