Question

三角形ABC中,AD⊥BC于D,若AB加CD＝AC加BD,证∠ABC＝∠ACB

Answer 1

设AB为x,AC为y,BD为m,CD为n.则x+n=y+m→x-m=y-n……(1)又因为AD⊥BC,所以x^2-m^2=y^2-n^2→(x+m)(x-m)=(y+n)(y-n)→x+m=y+n……(2),(1)+(2)得x=y即AB=AC.故∠ABC=∠ACB.