1.当AB=CB时:
(1)若AD=BD=CD:则∠ABD=∠A;∠CBD=∠C.
故:∠ABD+∠CBD=(∠ABD+∠A+∠CBD+∠C)/2=90度.
即∠ABC=90度;∠A=∠C=45度.
(2)若AD=AD;BC=DC.则:∠A=∠ABD,设∠A=∠ABD=X,则∠BDC=2X.
BC=DC,则∠CBD=∠CDB=2X.
∠A+∠C+∠ABC=180度,即X+X+3X=180度,X=36度.
故∠ABC=108度;∠A=∠C=36度.
2.当AB=AC时:
(1)若AD=DB=BC:则∠A=∠ABD;∠BDC=∠C.
与1.(2).同理相似可求得:∠A=36度;∠ABC=∠C=72度.
(2)若AD=DB;CD=CB:则∠A=∠ABD;∠CDB=∠CBD.
同理相似可求得:∠A=(180/7)度;∠ABC=∠C=(540/7)度.