Solution:
The triangles are similar to each other.
The key to this problem is that the 5 parts that
are congruent in the 2 triangles are not the
corresponding parts. Otherwise, the triangles
would be congruent by SSS or SAS...
All three pairs of angles must be congruent.
The three pairs of sides can not be congruent or
else it would be SSS.
Here is an example of how this can work:
Triangle ABC is similar to triangle DEF.
Triangle ABC Triangle DEF
------------ ------------
angle A = angle D
angle B = angle E
angle C = angle F
side AB = 18 side EF = 18
side AC = 12 side DE = 12
side BC = 27 side DF = 8
Thus, five pairs of parts are congruent, but the sixth
pair is not congruent.
The ratio of the the three pairs of
corresponding sides is 3:2.
AB BC AC 18 27 12
-- = -- = -- or -- = -- = --
DE EF DF 12 18 8
3
which all reduce to ---
2