In the following example, triangles ABC and DEF are congruent by SSS.
In his books Elements, Euclid showed
that for SAS, ASA, AAS and SSS, if three corresponding parts of
two triangles are congruent, then all six parts have corresponding
congruent parts. However, there are instances in which five of
the six parts of one triangle are congruent to five of the six
parts of another triangle without the triangles being congruent!
Consider the following pair of triangles. Five parts of one triangle
are congruent to five parts of the second triangle. But why are
they not congruent?