Question

三角形,角ABC=90度,AB=BC,AE是角平分线,CD垂直AE于D,可得CD=一半的AE,请说明理由

Answer 1

延长AB,CD交于F.

∠FDA=∠CDA=90°,AD=AD,∠FAD=∠CAD,

△FAD≌△CAD,∴DF=DC.

∠FBC=∠EBA=90°,BC=BA,∠F=∠BEA=90°-∠BAE,

△FBC≌△EBA,∴CF=AE.

CD=CF/2=AE/2.