If two triangles have the two sides equal to two sides respectively, and also have the base equal to the base, then they also have the angles equal which are contained by the equal straight lines.
Let triangles ABC and DEF have AB = DE, AC = DF, and BC = EF.
Apply triangle ABC to DEF so that B falls on E and BC on EF.
Since BC = EF, C coincides with F.
By Proposition 7, A must coincide with D.