第1个回答 2009-05-08
AB:AC=BD:DC A'B':A'C'=B'D':D'C'
AB=A'B' AC=A'C' AD=A'D'
AB:AC=A'B':A'C'=BD:DC=B'D':D'C'=K
AD^2=(AB+BD)(AC-DC)=A'D'^2=(A'B'+B'D')(A'C'-D'C')
所以 (AB+K*DC)(AC-DC)=(AB+k*D'C')(AC-D'C')
所以 -K*DC^2=-K*D'C'^2
DC=D'C' 同理 BD=B'D'
所以 BC=B'C'
所以ABC 与 A'B'C'全等