Question

八年级几何解析三角形ABC,AD是角BAC的角平分线已知AB加BD等于AC,求角B:角C.

Answer 1

(1)在AC上截取AE=AB,

∴ EC=AC-AE=AB+BD-AB=BD

∵ AD=AD,∠BAD=∠EAD,AB=AE,

∴△BAD≌△EAD,

∴BD=DE,(∠ABD=∠AED),

∴DE=EC,所以∠EDC=∠C

∴∠ABD=∠ABC=∠AED=∠C+∠EDC=2∠C