Question

已知：如图,直线AB,射线OC交于点O,OD平分∠BOC,OE平分∠AOC.试判断OD与OE是否互相垂直,请说明理由.

Answer 1

OD平分∠BOC,

∠DOC=(1/2)∠BOC

OE平分∠AOC,

∠EOC=(1/2)∠AOC

∠DOE=∠DOC+∠EOC=(1/2)∠BOC+(1/2)∠AOC

=(1/2)(∠BOC+∠AOC)

=1/2*180°

=90°

∴OD⊥OE