Question

ad,ae分别是 △abc的高和角平分线求角dae与角c-角b的关系,请证明

Answer 1

∠DAE=1/2(∠C-∠B).

证明：

∵AE平分∠BAC,

∴∠CAE=1/2∠BAC

=1/2(180°-∠B-∠C)

=90°-1/2∠B-1/2∠C,

∵AD⊥BC,∴∠CAD=90°-∠C,

∴∠DAE=∠CAE-∠CAD

=90°-1/2∠B-1/2∠C-(90°-∠C)

=1/2∠C-1/2∠B

=1/2(∠C-∠B).