如图,△ABC中,AB=AC,AD、CD分别是△ABC两个外角的平分线. (1)求证:AB=AD; (2)若∠B=60°,求证:四边形ABCD是菱形.
问题描述:
如图,△ABC中,AB=AC,AD、CD分别是△ABC两个外角的平分线.
(1)求证:AB=AD;
(2)若∠B=60°,求证:四边形ABCD是菱形.
答
(1)证明:∵AB=AC,∴∠B=∠ACB,∵AD平分∠FAC,∴∠FAD=12∠FAC,∵∠B+∠ACB=∠FAC,∴∠FAD=∠B,∴AD∥CB,∴∠D=∠DCE,∵CD平分∠ACE,∴∠ACD=∠DCE,∴∠D=∠ACD,∴AC=AD,∵AB=AC,∴AB=AD;(2)∵∠B...