For DE ⊥ AB and DF ⊥ AC, the vertical feet are E and F respectively. Because AD is the bisector of the angle BAC, DE=DF (the distances of points on the bisector of the angle are equal).
S△ABD= 1/2 *AB*DE ①
S△ACD= 1/2*AC*DF ②
①/② Available
S△ABD:S△ACD=AB:AC
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