It is known that in △ ABC and △ def, ab = De, BC = EF, ∠ BAC = ∠ EDF = 1000;

It is known that in △ ABC and △ def, ab = De, BC = EF, ∠ BAC = ∠ EDF = 1000;

prove:
BM is perpendicular to AC through B, and Ca extension line is perpendicular to M
Make en perpendicular to DF through E and cross FD extension line to n
So ∠ BMA = ∠ end = 90 degrees
Because ∠ BAC = ∠ EDF = 100 degrees
So ∠ BAM = ∠ EDN (equiangular complements are equal)
And because AB = De
So △ ABM ≌ △ den (corner side)
So BM = en, am = DN
And because BC = EF
So RT △ BMC ≌ RT △ eNf
So MC = NF
So MC - Ma = NF - nd
That is, AC = DF
And because AB = De, BC = EF
So △ ABC ≌ △ def (side)