Question

如图,△ABC∽△A'B'C',相似比为k,AD、A'D'分别是△ABC、△A'B'C'的角平分线.试说明AD/A'D'

Answer 1

相似,角相同,∠A=∠A‘,∠B=∠B‘,可用正弦定理证之.

在三角形△ABD与△A'B'D'中,由正弦定理有：AD/AB=sinB/sin(B+A/2),A'D'/A'B'=sinB'/sin(B'+A'/2),既有AD/AB=A'D'/A'B',AD/A'D'=AB/A'B'=k.