GivenAB=DE, AC=DF, ∠A=∠D.

Suppose you start from B, and walk along BA a certain distance a to A; then at A you turn at a certain angle into another road AC; then you walk along AC a certain distance b to C. Again you start from E, walk a distance a along ED; turn off at D into DF at the same angle as before; then walk the distance b along DF to F. Since you have gone through the same set of movements in the two cases, and since the same cause always produces the same result, the results in the two cases must be the same, that is, you will arrive in both cases, at the same distance from the starting point. Hence BC = EF.